Kyle Edmund stepped up in Andy Murray’s absence to give Great Britain the perfect start against Kazakhstan in a decisive Davis Cup group tie in Madrid.

Assured of a quarter-final place with a victory, Britain lead 1-0 in the three-rubber tie after Edmund won 6-3 6-3 against Mikhail Kukushkin.

British number one Dan Evans will put his team in the last eight if he beats Alexander Bublik later on Thursday.

Murray has been rested as he continues his comeback from hip surgery.

If Evans loses, Britain will have another chance to win the tie through Jamie Murray and Neal Skupski in a deciding doubles rubber which follows the second singles match.

Kazakhstan, backed by a rowdy set of supporters, need to fight back to win or they will be eliminated from the new-look 18-team finals tournament which is being played across the week in the Spanish capital.

Britain could still reach the last eight as one of the two best runners-up even if they are beaten by the Kazakhs, although it would only be a slim chance with Group B runners-up Russia already guaranteed to qualify ahead of them.

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Edmund rediscovers form to give GB advantage

Murray’s absence was unsurprising after the Scot laboured to a three-set win over Dutch world number 179 Tallon Griekspoor on Wednesday, which left him admitting he was not as sharp as he would like to be after taking a month off competitive tennis to spend with his new-born son and family.

That placed the pressure on 24-year-old Edmund to perform, at the end of a year in which he struggled for wins and tumbled down the world rankings as a result.

But Edmund, the 2018 Australian Open semi-finalist who has dropped to 69th in the world, outplayed 67th-ranked Kukushkin in a noisy Caja Magica.

Kukushkin was backed about 100 boisterous and colourful fans, armed with drums and a trombone like they were when their women’s team played Britain in the Fed Cup earlier this year.

However, that did not put off Edmund, who himself was well supported by a noisy contingent of Union Jack-waving British supporters, who have travelled to Madrid in their droves.

Edmund showed no signs of the troubles which have plagued him on the ATP Tour this year, hitting 10 aces and 23 winners in a dominant performance.

The Yorkshireman’s explosive forehand – his key weapon – was particularly destructive, helping him take his fourth chance in the decisive break of the first set and save two break points in the following game.

After breaking again for a 4-2 lead in the second set, he took eight of the last nine points to race through the closing stages, converting his first match point when Kukushkin hit a forehand long.

That meant Edmund won in just one hour and 15 minutes, leaving the celebrating British fans dancing in the stands, while finally silencing the Kazakhs.

“The atmosphere has been amazing, I think we have got the most travelling fans so amazing to get so many people coming here from Britain,” Edmund said.

“I couldn’t wait to get out here and it was such a buzz to thrive off the crowd.”

How Britain’s qualification hopes could pan out

Barcelona footballer Gerard Pique has overseen the transformation of the 119-year-old competition into a season-ending finals, which sees the 18 nations split into six groups of three.

The six group winners automatically qualify for the quarter-finals with the two best-placed runners-up joining them.

Britain’s 2-1 win over the Netherlands in their opening group match on Wednesday means they will top Group E by beating Kazahkstan.

• If Great Britain win the tie (either 2-1 or 3-0) they qualify for the quarter-finals as group winners
• If Great Britain lose the tie 2-1, they will not qualify as one of the two best runners-up
• If Britain lose 2-1 to the Kazakhs then their hopes of progressing go down to the percentage of matches won
• Following the win over the Netherlands, Britain have 2-1 record, meaning they would finish with a 3-3 (50%) match-win percentage
• That means they can’t overtake Russia, who are currently the leading second-placed team with a 4-2 (67%) match-win percentage
• A 50% match-win percentage for Britain would place them alongside Argentina and Belgium, meaning it would go down to a set-win percentage
• Britain currently have a 7-3 (70%) set record but if, in the best-case scenario, Evans and Murray/Skupski both lost 2-1 that would give them a 9-7 (56.25%) set record
• * Argentina, who are now guaranteed to finish as Group C runners-up after Germany won their opening rubber against Chile, have a 8-6 (57%) set record

Rafael Nadal’s Spain eased into the quarter-finals at the Davis Cup finals, beating a weakened Croatia to send the defending champions out of the event.

With Croatia missing Marin Cilic and Borna Coric, doubles specialist Nikola Mektic had to play singles against Roberto Bautista Agut, losing 6-1 6-3.

Nadal then beat Borna Gojo 6-4 6-3.

Meanwhile, Serbia, who won the Davis Cup in 2010, put themselves in pole position in Group A with a 3-0 victory over Japan at the Madrid event.

Filip Krajinovic defeated Yuichi Sugita 6-2 6-4, Novak Djokovic thrashed Yoshihito Nishioka 6-1 6-2, and Janko Tipsarevic and Viktor Troicki clinched a tight doubles match against Ben McLachlan and Yasutaka Uchiyama, winning 7-6 (7-5) 7-6 (7-4).

Germany also triumphed 3-0 as they defeated Argentina. Philipp Kohlschreiber battled back from a set down to defeat Guido Pella 1-6 6-3 6-4 and Jan-Lennard Struff was too good for Diego Schwartzman with a 6-3 7-6 (10-8) success.

In the doubles, the German pairing of Kevin Krawietz and Andreas Mies overcame Maximo Gonzalez and Leonardo Maye after the longest tie-break in Davis Cup history as they won 6-7 (4-7) 7-6 (7-2) 7-6 (20-18).

Great Britain’s near nine-hour tie with the Netherlands,which ended in a 2-1 victory for GB, meant that the tie between Australia and Belgium to decide who will win Group D started two hours later than scheduled.

Spain’s victory over Russia on Tuesday had finished in the early hours of Wednesday and a similarly late finish looked on the cards for both Australia v Belgium and the Group F match between the United States and Italy as questions over scheduling arose at the re-vamped competition.

The United States were at the centre of controversy after group winners Canada conceded their doubles rubber on Tuesday when they had an unassailable 2-0 lead.

It meant the US were given a 6-0 6-0 win for the doubles, which could potentially help them qualify for the last eight as one of the two best runners-up.

Organisers the ITF said three Canadian players had been declared unfit to play, but Britain’s Andy Murray was among critics of the decision to forfeit, saying: “I don’t think that’s good.

“So where Canada may have felt that that was a dead rubber in theory for them because they were already through, that could have implications to all of the teams potentially that might finish in second place.”

• GB win thrilling Davis Cup opener
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Andy Murray survived a scare against Dutch world number 179 Tallon Griekspoor before giving Great Britain a winning start at the inaugural Davis Cup finals in Madrid.

Murray, 32, lost the opener in the new best-of-three sets format before winning 6-7 (7-9) 6-4 7-6 (7-5).

The group stage tie continues when British number one Dan Evans plays Robin Haase later on Wednesday.

Jamie Murray and Neal Skupski will play in the doubles to round off the opener.

Britain, who won the 2015 Davis Cup in the previous format, have been drawn against the Netherlands and Kazakhstan – who they face on Thursday – in the group stage.

Eighteen nations are contesting a football-style knockout tournament for the first time to determine the Davis Cup champions, with the winners of the six groups and the two best-placed runners-up reaching the quarter-finals.

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• ‘Format had to change’ – Jamie Murray

Brilliant atmosphere & thrilling finale

Barcelona footballer Gerard Pique has overseen the transformation of the 119-year-old competition into the season-ending finals, which has been met with fierce criticism from some and doubts about the atmosphere such a format would create.

While Spain’s opening match on Tuesday night was unsurprisingly watched by a partisan and full crowd at the Caja Magica, some matches have struggled to attend spectators.

Britain’s opening tie against the Dutch was not expected to be one and so it proved as about 1,000 Union Jack-clad fans created a boisterous atmosphere on a 2,500-capacity third show court which was about three-quarters full by most estimates.

The crowd was given plenty of entertainment by Murray and Griekspoor in a gripping match full of ebbs and flows, a final-set tie-break providing a thrilling finale which eventually separated the pair.

Supporters from both nations were left standing on their feet and roaring their player towards victory in the tie-break, with Murray sealing the type of win he has earned throughout his illustrious career after two hours and 51 minutes.

“The atmosphere was one of the things players were worried about in a neutral venue but both sets of fans were fantastic,” Murray said.

The new Davis Cup format

Eighteen nations are split into six groups of three, with the group winners and two best-placed runners-up progressing to the quarter-finals.

The two semi-finals will be played on Saturday, 23 November with the two winners going through to the final on Sunday, 24 November.

Schedule – who plays when?

Group stage: Monday, 18 November – Thursday, 21 November

Quarter-finals: Thursday, 21 November – Friday, 22 November

Semi-finals: Saturday, 23 November

Final: Sunday, 24 November

More to follow.

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Judy Murray says it is a “massive honour” to be given a lifetime achievement award by UK Coaching for her services to tennis.

Murray, mother of Grand Slam-winners Andy and Jamie, has been coaching for 30 years, including a stint as Great Britain’s Fed Cup captain.

Most recently, the 60-year-old has invested her own money to launch the Miss-Hits tennis programme to teach girls worldwide to play the sport.

The ceremony is in London next month.

Murray said: “Having started as a volunteer at Dunblane Sports Club when my kids were toddlers, I’ve experienced every step of the coaching journey from local community club right up to Grand Slams, Olympics and Fed Cup, so I understand the importance of having great coaches at every stage and every level of the game.”

Jamie Murray is part of the Great Britain team competing in the inaugural Davis Cup finals and, in his latest BBC Sport column from Madrid, talks about the controversial new format, representing his country again alongside brother Andy, plus how Real Madrid tours, pool and ‘cornhole’ games have fostered team spirit.

Everyone in tennis was in agreement that the Davis Cup needed to change.

The top players weren’t able to commit to the event, not because they didn’t want to, or because they didn’t like the Davis Cup, it was just because it took so much time out of their schedule during the year.

If you got to the final it could be eight weeks in your year and with the fixtures always played right after the Grand Slams, ATP Finals or other big events, it meant the ties didn’t come at the right time of the calendar.

That is a shame because it is amazing event and, I think, when a large majority of tennis players look back on their careers, the matches they will remember will be the Davis Cup matches because they stir up the most emotion and have been played in front of cracking atmospheres. I’ll certainly remember them the most anyway.

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But the ITF had to make a change, they have made a change, some people don’t like it and some people do. But this is the first year since Barcelona footballer Gerard Pique and his Kosmos group got involved so we have to see how it goes.

From a player’s perspective, the format is pretty cool and it is fun to be here as a team along with 17 others, it is cool to see all the players together playing for their country and wearing their national colours.

There are a lot of good teams here, I know not all the top players in the world are playing, some didn’t qualify and a couple chose not to, but there are a lot of great teams and there should be a lot of great tennis this week.

It doesn’t surprise me that a lot of the top players are here, first and foremost because players love representing their countries, but also because there has been a huge injection of cash from Kosmos. There are definitely financial incentives for guys to come and play here.

I always thought 95% of the players would play if they qualified, why wouldn’t you? Financially it makes sense and you have the prestige of playing in the Davis Cup.

Most of all it is a fun week, you’re here with your friends, you’re part of a team.

‘We hope the stadiums will be packed’

There has been some concern about the size of the crowds and suggestions a few ties at the Caja Magica will be far from sold out.

I hope people do come out and support the event because it has the potential to be a great event.

It’s like the football World Cup, a lot of those matches aren’t necessarily glamour matches and the stadiums aren’t full.

I’m sure it’ll be the same here but for the real big matches we hope the stadiums will be packed and provide a great atmosphere which showcase potentially the best tournament in tennis.

I genuinely don’t how the fans will react and whether the crowds will improve as the tournament moves through the week and develops over the next few years.

Unless you’re Spanish, or you’re living here in Madrid, there is a considerable cost to come for potentially a week, but I understand that a fair few Brits will be here for our matches against the Netherlands on Wednesday and Kazakhstan on Thursday.

Madrid has a Masters tournament in May where you get the best 50 men and best 50 women competing so now the city has got a new event with not all the top 50 competing, and without the women, so it might not be as attractive for them to come and watch because they’ve already seen tennis a few months earlier.

I hope not but we will have to wait and see then go from there.

But as far as the event goes – the organisation, logistics and set-up – it has been great.

• What the new format looks like

‘I’m happy to be representing Britain again with my brother’

Of course, my younger brother Andy is part of Great Britain team again, only 10 months after he had a major hip operation which left him unsure whether he’d play again.

It is great to have him back playing and fit and healthy and committed to playing for Great Britain in the Davis Cup – and it boosts our chances in the competition.

It will be a lot of tennis for him in the next five days if we are to go through the tournament to the final, which will mean playing every day.

We’re always going to be a more dangerous team with him playing and if he performs to the level that we all know he is capable of then we have a great chance of going far.

Truthfully I’d never thought about whether we’d play together again in the Davis Cup during his injury struggles, but I know he loves playing and being part of a team so I’m happy he is back.

For us the motivation is playing for our country and getting together with a great team.

• Murray cautious of heavy schedule

‘The tourists at Real Madrid didn’t know what was happening!’

The British squad came out to Madrid last Wednesday and Leon Smith, our Davis Cup captain, has done a great job of creating a great team spirit among the team, not just the five players but all the support staff as well.

Leon makes sure when we turn up that we have a good, fun week and everybody enjoys it regardless of what the result is and that’s why I think we’ve had a lot of success in recent years.

He makes it fun for the players to come because he understands it can be an effort for the guys to play with another week out of the schedule.

We’ve done a few cool things around the city and a couple of days ago we went to the Santiago Bernabeu – Real Madrid’s stadium – that was great fun.

It is a nice tour – they’ve won everything haven’t they!

We saw the Ballon d’Ors, the Golden Boots, shirts of players from Alfredo di Stefano and Juanito to Ronaldo and Raul, we went into the dugouts and stood on the side of the pitch.

The other notable part of the tour was that we made Neal Skupski do his Davis Cup rookie speech in the Real Madrid press room!

He was supposed to do it at the official team dinner but it wasn’t possible so we got him unannounced in the press room.

He did the usual speech – thanking Leon for selecting him, what a great honour it was representing Britain, saying he was looking forward to playing – but the big difference was the location and that there were also a few tourists watching who didn’t know what was going on. No pressure!

We’ve also been having fun with a pool competition, we had the semi-finals and final on Tuesday night. Leon beat me and Andy – he hasn’t shut up about that – so I know he’s in the semi-finals.

The most fun activity is cornhole – an American game where you have a wooden board with a hole in the middle and you have to try and throw a bag in there – because it is mass participation and we have good fun.

I’m sure other sports teams do it but all of these activities have been a good way for team bonding and build our camaraderie going into the tournament.

Let’s hope we can go all the way to Sunday’s final!

Jamie Murray was speaking to BBC Sport’s Jonathan Jurejko in Madrid.