More than two-thirds of the UK public believe the £8.77bn cost of the London 2012 Olympics was worth the money, according to a BBC survey.

Of the 3,218 adults polled, 74% would also welcome the Games back to Britain.

The results show people are more active since the Olympics, with 11% saying they exercise more than a year ago, rising to 24% for those aged 18 to 24.

The London showpiece, together with the Paralympics, cost more than three times the original budget of £2.4bn.

Recent government research suggests the UK economy received a £9.9bn boost in trade and investment from staging the Games.

A year on from the start of London 2012, the survey, conducted by ComRes, aims to understand public perceptions of Olympic legacy and what impact the event has had on communities.

It found that, of those polled:

  • 11% said they are more active as a result of the Games;
  • 32% said the Games had a positive impact on sports facilities;
  • 22% said the Games had improved their local economy;
  • 21% said the Games had resulted in improved public services.

Graphic about what impact the Olympic Games had on different areas of the UK

One of London's legacy promises  was to "inspire a generation".

The poll shows young adults are the most enthusiastic about the Games returning to Britain, with 82% of those aged 18 to 24 keen on the idea.

On the issue of cost, 69% of people responded positively to this use of public money, although a higher percentage of those came from the South East, where most events at the Games were staged, than elsewhere.

In the BBC South East region, 78% were happy with the cost, compared with 63% in BBC Yorkshire.

On the issue of people becoming more active, the last Labour government pledged that two million  would play more sport as a result of the Olympics. That target was later revised to one million.

People in the BBC North East and BBC Cumbria regions are likely to have been the most active, according to the survey, with people in the BBC South West and BBC West Midlands regions the least.

However, 88% of those polled said their activity levels had not changed following the Games.

Graphic about whether people are more active after the Olympics and whether people felt the Games were money well spent

That statistic chimes with a Sport England study, which shows that the number of people participating in sport once a week fell by 200,000 between October 2012 and April 2013.

Sport England points out that, according to their figures, there are still 1.4 million more people playing sport than in 2005, when London won the right to stage the 2012 Olympics and Paralympics.

Sports Minister Hugh Robertson said: "We've made an incredibly good start [to building a legacy] but I would be the first to admit there is an awful lot left to do. I don't think we'll be able to make a judgement on the legacy until three years after the Olympics, maybe five, and probably, if we are being really honest, until a decade has passed since London 2012.

"We can prove that there are 1.4 million extra people playing sport who were not playing sport when we won the bid. Everything I hear from the individual sports tells me that the actual figure is much larger than that.

"If you had asked me a year ago about what the legacy would look like, I would have said it was about the increase and boost to the economy and regeneration of Stratford.

"But the single most important legacy we have got from London 2012 is that everywhere I go around the world, people still reminisce about the Games and say 'well done' for laying on the best Olympics and Paralympics of all time. That is a calling card that is worth a lot in the international market."

Image of David Bond David Bond BBC sports editor

As Rebecca Adlington says, legacy is a difficult issue because people expect to see results instantly.

One year on it is worth giving credit for the progress that has been made. Work on transforming the Olympic Park into a new community is under way and the venues all have their futures sorted.

But getting the country more active remains the biggest challenge. As the poll shows, changing sporting habits could take years. The worry is that the further one gets from the Games, the more momentum is lost.

Double Olympic champion Rebecca Adlington, who quit competitive swimming after winning two bronze medals in London, added: "Legacy is a difficult subject for people to talk about because people want to see it happening straight away.

"For me, what will be a nice moment is, in 10 or 15 years, seeing someone come out of a pool or the velodrome, doing their interviews and saying, 'I was inspired by London; it got me into sport'. That is what legacy is about."

A key part of the London 2012 legacy plan  focused on sports facilities. Of those polled, 32% said they had noticed an improvement, although more than half said there had been no impact at all.

One in five people polled reported an additional benefit to their local economy and public services.

However, 69% said there has been no impact on public services, while 67% said they have not witnessed any impact on the local economy.

Tim Lamb, chief executive of the Sport and Recreation Alliance, the organisation responsible for the governing and representative bodies of sport and recreation in the UK, said: "It's very important to keep the momentum going.

"We're going to have to find a way of investing in facilities in our sports clubs, making sure that when facilities are hired for sporting activity they are affordable, making sure that clubs and people playing sport have got the right equipment.

"It's about spending money more wisely and recognising the enormous social benefits that sport has. It is obviously good for your health, it can help to reduce anti-social behaviour, it's proven to improve academic attainment and it can help build community cohesion. It's a very low-cost way of tackling some of the key social problems that we've got in this country."

Between 5 and 21 July 2013, telephone interviews were conducted with 3,218 adults and the data weighted to be representative of all United Kingdom adults aged 18 and over.