Anne Keothavong was finally able to celebrate World Group play-off success at the fifth time of asking as Great Britain returned to the Fed Cup's top table for the first time in 26 years.

It was a weekend full of drama at London's Copper Box and Johanna Konta and Katie Boulter both produced comeback wins to earn Britain a 3-1 victory overall.

Britain had fallen at this hurdle four times in the last seven years, with Keothavong involved in all of them, twice as player and twice as captain.

The 35-year-old, who grew up nearby in Hackney, said with a big smile: "Finally. I'm ecstatic. I'm ecstatic for the team. I'm just totally in awe of these women. It was such an incredible effort by everyone.

"The performances this weekend, the courage they showed out there. We kept putting ourselves in this position to have a chance of getting through this play-off but I really feel like having home advantage this time made all the difference."

The zonal ties in Bath in February were the first time Britain had played at home in Fed Cup since 1993 – with the previous play-offs taking the team to Sweden, Argentina, Romania and Japan – and there was a rousing atmosphere all weekend, helped by a noisy Kazakh band.

The tie was level at 1-1 overnight after Boulter was unable to take three match points in a heartbreaking defeat to Kazakh number one Yulia Putintseva.

The visitors looked set to take a 2-1 lead when Putintseva led Konta by 4-1 and two breaks of serve in the deciding set of Sunday's first rubber, only for the British number one to win the last four games in a 4-6 6-2 7-5 victory.

It was Konta's 11th singles success in a row in the competition and meant victory for Boulter against Zarina Diyas would seal the deal.

It had been in doubt whether the 22-year-old would even take to the court after she picked up an injury during Saturday's match, which a telltale hot water bottle revealed to be to her right hip and lower back area.

She was still using the hot water bottle during changes of ends, and a deciding doubles rubber was looming when she trailed by a set and a break to 107th-ranked Diyas, but Boulter has proved herself quite the competitor in her fledgling career and she battled back to win 6-7 (1) 6-4 6-1.

Boulter said of her injury: "It was hurting a little bit yesterday but I knew if I was mentally strong then I could get through anything."

She and Keothavong both admitted they had not slept on Saturday night but the disappointment did not weigh heavily.

"It's what we have to do," she said. "It's part of tennis. We all have good days and bad days and I'm going to fight and I'm going to get up for the next match no matter what the circumstances are. I'm proud of myself today bouncing back like I did."

Konta has been a stalwart of the team since making her debut in 2013, and the relief and delight were as palpable for her as for Keothavong.

"We've been in this position for the last three years, and even before that," she said. "I've definitely dreamed of wanting to be part of the team that finally is able to get through this hurdle and to battle whatever comes next. I'm so proud of everyone."

The victory currently secures Britain a place in World Group II, although the format of the competition for next season has not yet been decided.

Proposals for a 12-team finals in the mould of the revamped Davis Cup are reportedly at an advanced stage.

Keothavong revealed she has not been given a chance to voice her opinion on the matter but will leave those concerns for another day.

"I think right now it's important for us to enjoy this moment," she said. "For a lot of tennis players, it's difficult to enjoy the victory because you're so worried about what's happening the next week. We've worked hard for this and, whatever the ITF decide, will be."