Speaking before the London Games’ closing ceremony yesterday, Cameron said that UK Sport will receive around £125m a year over the next four years to distribute to sports’ governing bodies, with £40m coming from government. His remarks followed the most successful performance by British athletes for more than a century. Team GB won a total of 65 medals, of which 29 were gold.

The prime minister said the funding, which will also support Paralympic GB athletes, would provide ‘certainty’ for sport bodies, allowing them to plan to emulate or better 2012’s record medal haul.

Cameron said: ‘The motto of these games has been “inspire a generation”. Nothing has been more inspirational than seeing our elite athletes win gold this summer,’ he said.

‘There’s a direct link between elite success and participation in sport. I want one of the legacies of these games to be our athletes triumphing in Rio in 2016, and in future Olympic Games. Guaranteeing this funding will help ensure that happens.’

UK Sport had already been allocated exchequer funding for elite athletes up to the end of the current Spending Review period in 2014/15, covering the first half of the four years leading up to Rio. Funding is now being committed to 2016/17, to give athletes and governing bodies financial certainty.

The government’s contribution in 2015/16 and 2016/17 will be added to the projected £87m National Lottery funding expected in each year, which will help athletes train full-time in their sports.

Funded athletes will also be asked to offer up to five days a year of their time to school sport events.

UK Sport chair Baroness Campbell said that London 2012 had ‘put the UK on the map as a high performance nation with the talent to compete with the best nations of the world’.

She added: ‘The government’s announcement to maintain funding in our high performance system demonstrates vision and commitment to sustain this level of high performance beyond London on to Rio and beyond – a true legacy of the games.’

Athletes also welcomed the funding announcement. Britain’s most successful Olympian, six-time gold medallist Sir Chris Hoy, said: ‘I am old enough to remember a time when things were run on a shoestring budget before National Lottery and government investment transformed British Olympic sport. Having these guarantees for the future will be a huge boost for all the athletes aiming to win medals at Rio 2016 and proves we are serious about building a strong legacy from London 2012.’

Jessica Ennis, who won gold in the heptathlon in London, added that it was ‘fantastic that the government has made a big commitment to invest in British Olympic sport’.

She said: ‘Competing in the Olympic Stadium was unforgettable and demonstrated the unique and amazing power of sport to provide those inspirational moments that can bring a nation together. Continued funding means we can seize the opportunity to build a lasting legacy from what has been an amazing London Olympics.’