Almost four-fifths of people in some of Britain’s largest cities want road space taken away from cars and given to bikes, according to a new poll from Sustrans. I’m not at all surprised. Whenever we proposed the same thing in London, where I was cycling commissioner until last year, we got the same response.

Every single one of the cycle superhighway schemes now open in the capital got between 60% and 85% public support, in our own statutory consultations and in independent, professional opinion polls. Once the new routes opened, that support translated into astonishing levels of usage. In the first six months, the number of cyclists on the roads served by the new separated lanes went up by more than half. The bike lane on Blackfriars bridge, which takes up a fifth of the roadspace, now carries 70% of the bridge’s rush-hour traffic.

There’s an Eiger of evidence that cycling improvements are popular. Why, then, do they so seldom happen?

Partly it’s because politicians confuse noise with numbers. Cycling schemes create a lot of noise. Our opponents would spend busy weeks organising petitions, holding demonstrations and comparing bike lanes to the Luftwaffe in their effects on the capital. But almost every time the consultation results came back, the nimbies found that they lacked the numbers. In this year’s election, the MP who campaigned hardest against our cycling schemes, the Enfield Tory David Burrowes, lost his seat. In Walthamstow, where fire and brimstone was directed at our and the Labour council’s “mini-Holland” cycling project, Labour was re-elected with 80% of the vote.

Partly it’s because the people making the decisions drive, or are driven, and imagine that everyone else must too. Our most strident opposition came from taxis and the people who use them: MPs, ministers, City grandees. But in London and several other inner cities, almost no one drives: only 5% of commuter journeys into central London are done by car, and only 7% of Londoners drive even once a week in the centre.

It’s also partly because cyclists are seen as a separate species, unconnected to the rest of the transport system. But every new cyclist is freeing space on the roads or on public transport for others who do not cycle. Everyone who cycles improves not just their own health, but everybody else’s, by reducing pollution, traffic danger and noise. If bike lanes benefited only the relatively few who already cycled they would not, of course, win such wide support.

‘The mayor of London, Sadiq Khan, is still finding it hard to make even quite easy decisions about bikes and traffic.’ Photograph: Nick Ansell/PA

Cycling schemes are not hard in engineering terms. They succeed or fail on the politics. For those places outside the capital now contemplating change, there are several things you can do to increase your chances of success, and reduce your opponents’ chances.

Before you make any specific proposal, prepare the ground. Try to persuade people of the need for change: if the roads are full, what would you rather have, new roads cutting through your city, or better use of the roads you’ve already got? Lay out an attractive alternative to the status quo that people could support.

Relate cycling and traffic reduction to things that touch people’s lives. We asked doctors and emergency staff – more trusted by the public than politicians – to talk about how cycling could make people healthier and help the NHS survive. Another city related it to pollution, putting air quality monitors outside schools to show parents how much danger their kids were in.

We worked out every aspect of a proposal in detail before we presented it, anticipating and pre-empting likely objections. We looked at parking, for instance, in a very granular way, examining exactly who parked where, for how long and why. We thought how we could accommodate as many of those needs as possible – say, by moving a parking space round the corner, rather than just scrapping it – without compromising the essential principles of the scheme.

We had data ready to counter fears and misrepresentations. We demonstrated through polling that our opponents were in the minority. Every time they produced a businessperson or a politician to counter the scheme, we produced three or four to back it. We ignored wrecking objections but accommodated reasonable ones, changing some of the schemes to reduce their impact.

In the end, however, all this relies on having a political leader who is actually willing to lead. And that species is in disappointingly short supply. In my London experience, some were superb but most, Labour and Tory, wanted only to talk about promoting cycling. When it came to doing anything much, their resolve faltered.

More than 18 months into his mayoralty of London, Sadiq Khan is still finding it hard to make even quite easy decisions about bikes and traffic. He’s still wringing his hands about whether to close Regent’s Park to rat-running cars – a cycling scheme with big non-cycling benefits and substantial majority support.

Indeed, almost all the cycling projects Khan inherited from his predecessor – designed, consulted on and publicly approved by large margins – have spent the last year and a half on hold. No new schemes have yet been approved. The poor man even took nearly a year to scrap the almost friend-free Garden Bridge, which really should have been a day-one decision.

Voters may support cycling, but on most polls it would be well below health, the economy, transport generally or the environment in most people’s priority lists. This, no doubt, is why Khan and other fence-sitters treat cycling as marginal, and not worth spending their political capital on. But that’s a mistake, because cycling isn’t just popular: it’s a key that unlocks all those other issues.

• Andrew Gilligan is the former cycling commissioner for London