The government is to counter criticism that it is failing to deliver on the promises that helped win the 2012 Olympic Games for London by appointing a "sports legacy tsar", to get more people participating in sport and help attract private sector investment.

Ministers are looking for a high-profile figure who could be a former Olympic athlete or an influential name who has experience of running a sporting body.

With the Olympic flame due to be lit in the new stadium in Stratford, east London, three years from tomorrow, there is increasing optimism that organisers will deliver the games on time and within the £9.3bn budget, despite the impact of the recession. But opposition MPs and senior sports figures have told the Guardian that there remain serious questions over the legacy of the 2012 Games. In particular, there are concerns over promises to use the Olympics to increase sporting activity and fight obesity.

Critics claim that "four years have been wasted" in devising a strategy to deliver on the promise of getting 1 million people taking part in more sport by 2012 and a broader pledge to get 1 million more participating in physical activity, including walking and gardening.

Organisations including the British Olympic Association and the CCPR (Central Council of Physical Recreation), which represents hundreds of governing bodies, have voiced concerns that plans to use the Olympics to make a "once in a lifetime" change in the population's sporting habits are yet to have any impact at grassroots level. The shadow sports minister, Hugh Robertson, said: "The lack of a proper strategy for delivering our participation promises is the single biggest problem with the Olympics."

The Liberal Democrat Olympic spokesman, Tom Brake, said "alarm bells must be ringing in government", which "may have bitten off more than it can chew". The CCPR chair, Brigid Simmonds, added: "We have been saying for some time that the Olympics will have a long sunrise and a very short sunset. If we don't get it right, this huge opportunity will be lost. With three years to go, let's grasp it and let's get on with it." In response, it is understood that the sports minister, Gerry Sutcliffe, who remains confident that the targets can be achieved, plans to convene a new team led by a "legacy tsar" to co-ordinate sport participation.

The government believes that it has put all the necessary building blocks in place, including getting the various agencies working harmoniously and doubling sports funding in the three years since 2005, but acknowledges that a more co-ordinated national approach is required.

"Some regions are getting on and doing it and others are sitting back and waiting for something to happen," Sutcliffe said. "It's got to be about inspiration as well. The athletes need to be out in their communities inspiring people."

It will also co-ordinate a drive to get private backers involved in the legacy push. Adidas will announce that it is rolling out its "sportszone" concept around the country following a trial in London, and there are hopes that other Olympic sponsors will want to get involved with legacy projects. Figures released last week by Sport England, the body charged with delivering the 1 million participation increase and investing £480m of lottery and public funds in grassroots sport between 2009 and 2013, revealed that progress appeared to have stalled.

Quarterly figures showed that of 31 sports measured according to how many people played them at least once a week, only table tennis recorded an increase. Nine - including swimming, football, gymnastics and rowing - showed a decline and the rest showed no change.

In order to achieve its target, Sport England must boost the 6.8 million people playing sport for 30 minutes at least three times a week by 1 million. The other 1 million, to be delivered through other government agencies including the National Health Service, must be doing some form of physical activity for 30 minutes at least three times a week. Sport England argues that the quarterly survey is merely a guide and that the next annual survey, due in December, will give a clearer idea of progress under a plan launched earlier this year to invest the bulk of its lottery and public funds directly through sport governing bodies.

It was partly the bold legacy promises made by London Organising Committee chairman, Seb Coe, that the Olympics would transform the East End of London, inspire a generation of young people through sport and deliver health benefits for the entire nation that helped convince International Olympic Committee members to vote for the city in 2005.