Only 24% think their support for sport in schools and communities has increased since the Olympics and Paralympics.
The survey of 2000 people for a Sunday newspaper followed recrimination on failure of legacy from sports cut adrift from funding. Labour claimed legacy was "in tatters". Well, they would, wouldn't they? But it was surely no coincidence that the Prime Minister and his perceived leadership rival Boris Johnson mounted a rare display of unity, going on a joint offensive to refute the claims.
The survey, which had respondents from across Scotland, England, and Wales, was damning. It came as elite sportsmen such as the double gold medallist Mo Farah and the NBA basketball icon Luol Deng castigated the government for reductions in budgets ranging from school sport to elite performance.
Farah's wife, Tania, criticised cuts in primary school physical education and school sports partnerships. Deng attacked the refusal of UK Sport to bankroll a squad for the 2016 Olympics. UKS has since agreed to fund the squad for a year, before reviewing progress. Sports including volleyball and table tennis, rejected once again, seem likely to lodge formal appeals.
Undeniably, some legacy targets have been missed. There is notable failure to maintain investment in some sports, failure to meet school physical education targets and government vandalism of school sport partnerships that are envied around the world.
Yet legacy thrives, with booming participation and enthusiasm for sport in the wake of 2012. Entries for the London Marathon (the world's biggest marathon) and the Great North Run (the world's biggest half-marathon) continue to rise, while the Great Scottish Run last autumn enjoyed a record entry.
Glasgow is certainly keeping sport and recreation at the top of the agenda. Glasgow Life report that attendance at their sport facilities last year was up 8% to almost 6m. There has been a big surge in membership of the Glasgow Club (people using the city's 25 fitness facilities); a steady increase in demand for places on sport development programmes (just short of 750,000 attendances last year); and a 15,000 rise in numbers on the free-swim programme, to 270,000.
They believe this is all part of the Olympic legacy, but also helped by the 2014 Commonwealth Games. "Another key legacy is the ability to bid to bring the Youth Olympic Games to Glasgow in 2018," said a spokesperson. Spectating is at record levels. The Sir Chris Hoy Velodrome sold out in just 25 minutes for the UCI Track Cycling World Cup which attracted 20,000 people to the five sessions, and the Revolution cycling event was also at capacity.
The World Cup gymnastics at the Emirates sold out. Attendance surpassed the previous year's two-day total at the Kelvin Hall, and last month's indoor athletics event attracted double the previous Kelvin Hall record. Record crowds attended the national badminton championships and World Premier Club Challenge netball.
Entries for this year's Virgin London Marathon have never poured in quicker. They reached the ballot maximum (125,000) in just over 17 hours last April, before Olympic fever had even peaked, beating the previous record by 20 hours. Registrations for the Ride London cycle festival have also boomed.
Applications for the Great Scottish Run and BUPA Great Women's 10k in Glasgow have only recently opened but numbers are "encouraging", said Dave Hart, communications director of Nova International who organise them in partnership with Glasgow Life.
The GSR has grown from 20,868 entries in 2009 to 23,386 last year. Entries for the women's 10k dipped slightly last year, but it remains the biggest in Britain. Nova also organise the Great North Run, for which applications closed on Monday. "They are significantly up on last year's 100,000, which produced a record field," Hart added. "We operate a reminder service –emailing people when entries open – and that was up 20%. "We also do the Great North Swim Series, and entries for that are ahead of previous years. Our reminder service for the Great Manchester Cycle [Britain's biggest timed ride] has also grown significantly higher, which suggests entries for that will also increase."
The public appetite for sport seems unabated. When TV figures dropped after the Olympics, the televised GNR audience last October increased. And volunteers – they are critical to the success of 2012 – cannot get enough of it. Sport could not function without them; at least that part of the Big Society is flourishing.
Hart pays tribute, saying: "We have our own band of volunteers who return year after year. We are in our 33rd year, and we have guys who were there at the start."
Another leading mass participation sports events company, Human Race, organise 60 events annually, with more than 70,000 competitors. They recently surveyed 1500 people on legacy. More than 76% feel more inspired to participate, mostly in cycling and triathlon, and 87.7% feel performances such as those of Victoria Pendleton and Jessica Ennis will inspire more female participation. They cite evidence from their women-only events. The two highest-attended cycling events (supported by Pendleton) took place after the Olympics and enjoyed particularly significant growth.
They report a post-Olympic entry spike, with their first event of 2013, the Iceman (a duathlon and trail race), attracting 789 participants, up from 630 last year.
The public is on-message on legacy. It is central government who are letting the side down.