Laura Kenny became the first British woman to win gold at three Olympic Games as she and Katie Archibald were crowned madison champions in Tokyo.

“I’ve never wanted to win a medal so much in all my life,” said Kenny, the most successful female Olympic cyclist.

Jack Carlin then won individual sprint bronze for his second medal of the Games and Team GB’s fifth on the track.

He won team sprint silver earlier in the week alongside Jason Kenny and Ryan Owens, while Laura Kenny and Archibald won team pursuit silver.

Their madison gold on Friday follows Matt Walls’ victory in the men’s omnium the previous day.

The women’s madison was added to the Olympic programme for the first time at Tokyo 2020.

“I messaged [husband] Jason and said I feel like my Olympics ends today,” said Kenny. “I love the team pursuit but I felt relief when it was over because this was the one race I wanted to win – I just feel so relieved.”

Archibald added: “I’ve been dreaming about having this conversation – I’ve never wanted something so much, I’ve never been so nervous but we’ve been so clinical with our approach.

“We had a change of coach last year for this event. We’re going for the all round and trying to spread between events and it feels so satisfying for it to come off.”

Kenny and Archibald deliver masterclass

Archibald won World Championship madison gold in 2018 before she and Kenny teamed up for European silver in the event the following year.

But their performance in Tokyo was a masterclass in madison racing, winning the three opening sprints of the 120-lap, 30km race.

In total, they won 10 of the 12 sprints on offer and gained a lap – earning 20 points – alongside Denmark and the Russian Olympic Committee, who won silver and bronze respectively.

But such was Kenny and Archibald’s dominance that they finished with more than double the Danes’ points, Amalie Dideriksen and Julie Leth ending their race on 35 points while the ROC had just 26.

Dutch world champions Amy Pieters and Kirsten Wild finished off the podium, forced to settle for fourth after being involved in a crash.

Kenny and Archibald credited coach Monica Greenwood – who took over coaching the endurance squad in December – for their win, revealing they had been training against GB’s men’s under-23 squad to perfect their madison plan.

Kenny’s gold was her first as a mother, having welcomed son Albie in August 2017.

“All week I’ve been saying please don’t ask me about Albie – I’ve never missed him so much,” she told BBC Sport.

“But I couldn’t do it without these girls. With Katie I feel like I’m racing with a sister – I’m so grateful to have her here and her support. I couldn’t have done it without her.”

She later said: “When I fell pregnant, there was a moment two months into the pregnancy where I woke up and said to Jason ‘I can’t do this, I’m not going to be able to carry on [with cycling], there’s just no way.’ And here we are.”

Carlin takes sprint bronze

Earlier in the week, Jason Kenny had tipped team-mate Carlin for a medal in the individual sprint and that prediction came good in the bronze medal race.

The Scot had earlier lost in two legs to Dutch world champion and eventual gold medallist Harrie Lavreysen in the semi-finals, meaning he would take on Denis Dmitriev of the Russian Olympic Committee in the race for the final step on the podium.

Carlin comprehensively beat the Rio 2016 bronze medallist in the first race, crossing the line almost half a second before Dmitriev.

The second race, however, was much closer, Carlin just holding on to pip his opponent to the line by 0.015 seconds.

“Tough day today,” he said. “I didn’t feel like I had the same legs as yesterday but I gave it my all and managed to come away with something.”

Carlin took up cycling after breaking both ankles while playing football, needing a non-contact sporting option during his recovery, only to go on to break his wrist on his first track session.

Lavreysen beat compatriot Jeffrey Hoogland over three legs in the gold medal race.