When Jacques Rogge and Lord Coe closed the London Olympics, the loudest cheer was reserved not for the athletes – though the roar was deafening – nor for the organisers, who received an almost equally generous hand, but for the volunteers – all 70,000 of them. Or should I say, immodestly, us? The warm public embrace in which we volunteers have luxuriated – and which will surely last through the Paralympics – became a phenomenon of the Games. And the big question now – as big as David Cameron's Big Society – is whether the volunteering, like the sport, can "inspire a generation".

Why was there so much public enthusiasm? Pleasant surprise might be one explanation. For the Olympics, you have to have athletes, you have to have venues, and you have to have organisers. But the volunteers seemed to appear out of nowhere as a sort of bonus. The capital was suddenly speckled with clusters of pink- and-purple people, who were welcoming and polite – and the delight was mutual. London was transformed from an impersonal and at times threatening mega-city into somewhere more manageable and humane. You can say what you like about our uniforms, but you can't say you could not see us, and our kit conferred a certain sense of responsibility.

Just being there, I think, helped to create an atmosphere of safety and goodwill. But we were hardly alone. There were the police, visible but not at all threatening, in their Royal-Jubilee, Dixon-of-Dock-Green mode. There were the troops, in their fatigues and berets, giving a whole new look to Cool Britannia. The salutary effect of an official, but benign and common-sensical, presence is worth examining. With the closure of police stations, town halls and ticket offices, it is something our cities have progressively lost. Politicians, nationally and locally, should consider how it might somehow be restored.

Volunteers came from all ages and backgrounds. There might never have been such a cross-section of people cooperating since National Service was abolished. We really were a mirror of Britain. Some of my favourites were the mostly young people staffing the pedestrian crossings, trying to dissuade the huge crowds from trying to compete with a London bus. With their loud-hailers, cries of "Lad-eez and Gentlemen, careful now", "Wait for the green man", they were a splendid advert for young Britain, proof that courtesy, wit and a sense of responsibility has been hidden somewhere beyond the rioters and the Neets. They perfectly illustrated the notion that if you make people feel useful, they will rise to the occasion.

But will that spirit last? Will the volunteer army of the Olympics stick around to help build Mr Cameron's Big Society, and even if its foot soldiers don't, might they not have set an example that others will follow? And here, I regret to say – despite the reported surge in people volunteering to help with sports clubs in the immediate wake of the Olympics or offering a "Jubilee hour" of their time – I am less optimistic.

London 2012 was a glorious one-off, but a one-off nonetheless. Some have cited "glamour" as a motivation for the volunteers, but to me it looked more like a conjunction of individual Britons wanting to counter some of the negative impressions some visitors take away from this country, coupled with the conviction that nothing like this would happen again in our lifetime. There was a collective determination to get out there and do something, and the organisational framework set up for the Olympics made it possible. You didn't have to belong to a sports club, and you didn't have to "know someone". But the scale of the operation was vast, and it is hard to see how anything quite like it can be sustained.

The uniqueness of the undertaking meant that we really were – as novices – all in it together. Which has, alas, already touched off resentment on the part of existing good causes that the Olympics volunteers are getting all the glory (for what, in my case at least, was a mere 25 hours spread over five days), while many of their unpaid recruits have been beavering away for years with maximum dedication and minimal recognition. So let me apologise: to an extent, it was our visibility, and the surprise element, that "made" us. But I would hazard, too, that others could take lessons from the Olympics about flexibility and openness. Worthiness and cliquishness are forbidding.

These are not the only reasons why the Olympic volunteers may not report for a new tour of duty with the alacrity that is hoped – though our involvement has helped create a huge database of the willing! Serious volunteering requires regular and long-term commitments of time – time that is often in short supply. Many Olympic volunteers are students or retired people, some of whom already volunteer, or teachers (no comment about holidays). But many were using their annual leave. Volunteering for even an evening a week is more than many – with work, family and other obligations – can guarantee, even if we could afford it.

Another distinctive aspect of the Olympics was the feeling that we were doing something that would not have been done without us. And while the same might be said of helping in hospitals or care homes, or with literacy programmes or advice centres, there will be those – and I am among them – who feel that the UK is not America, and that there are some things the State should do and be prepared to pay for. The borderline will fall in different places for different people, but the suspicion about the Big Society is that it is driven by government and will end up filling holes in the State.

I don't at all exclude an Olympic effect on volunteering, especially in sport. And I would be delighted if someone – who? – set up a spin-off volunteer effort to offer information and directions in and around the capital during the tourist season. And I am delighted if the Olympic volunteers have helped reaffirm Cameron's faith in the generous spirit of Britons – as they have mine. But he would do well to keep quiet about it. Signing up to the Prime Minister's pet project is not what most of us had in mind when we applied to help with the Olympics all those months ago. And if he tries to co-opt us, it could turn us off the whole idea.

m.dejevsky@independent.co.uk