“Training” might be overstating it. Right now I’m not in training for anything, and nor, to my knowledge, are any of the others – Lewis, Charlie, and Graham.

We’re here to play.

In a moment or two, I see Lewis approaching. Pretty soon we are quorate, and the ride can begin. The four of us head to the Outer Circle – Regent’s Park’s perimeter road, measuring a little under three miles and, for many years now, an unofficial cycle training route. A wide thoroughfare where greenery abounds and vehicles and traffic lights are relatively scarce, it’s a unique facility in central London, which amounts to a secret cycling idyll.

Not that it’s so secret any more. I started making bike trips to Regent’s more than 10 years ago. In those days, cycling of this kind was a relatively obscure subculture. Now it’s mainstream, and in pre-work hours the Outer Circle is thronged with men and women on two wheels.

Pay a visit any time between 6.30 and 8.30 in the morning and you’ll see us – dozens and dozens of Lycra-clad figures on our not-inexpensive road bikes, riding mostly in groups, some as big as 20- or 30-strong. We aren’t going anywhere. We’re just riding the circuit, getting our heart rates up, feeling the speed, revelling in the sensation, trying to improve, or just stay fit. The ride is an end in itself. It serves no outward purpose. It’s the very essence of play.

“Regent’s is an arena,” is how Graham sees it, “replicating in miniature the aspects of a much bigger ride.” It has fast stretches, corners, changing vistas, even a “climb” – the drag up the east side when travelling anti-clockwise, which is the direction the vast majority of cyclists choose because it’s the safer, inside option.

The south east corner of the Outer Circle – the point closest to the Euston Road – is, for my group, where the lap begins. Then it’s up the east side drag – you can really hurt yourself on that stretch – before the road flattens and bends to the left and takes you past London Zoo, then dead straight and flat for around 500 metres, through a long left-hander past the US ambassador’s residence, Winfield House, and descending to the Regent’s Park mosque. The final stretch passes the top of Baker Street, runs parallel with the Marylebone Road and then it’s back to where you started.

How fast was that one, you wonder? But you won’t know until you’ve checked your Strava tracking app at the end of the ride. What you do know, as Graham says, is that the park is beautiful and there’s camaraderie in the group.

As with the parkour phenomenon of urban running, in which the obstacles of the built environment are turned to advantage, so it is with cycling and Regent’s Park. The Outer Circle wasn’t laid out with cyclists in mind. We discovered it, we saw its potential, we shaped it for our purposes, and turned it into our playground.

The game we invented has its rules. Strangers hook up all the time. My group will jump on to the back of other groups. Other cyclists will jump onto the back of us. Most of us reckon we know how to conduct ourselves riding in tight groups, which is much the most effective way to ride at speed. No random braking, maintain your line, overtake smoothly, do your turn at the front. Or if you don’t want to do a turn on the front – if the pace is just too high – then stay on the back.

The way that one can coexist with people one doesn’t know – in close proximity, in a state of mutual co-operation, mutual dependency – is what raises Regent’s to the level of social experiment. Going round Regent’s, I will latch on to someone’s wheel and for a few minutes we are as one, this stranger and I, until one of us drops off, or a bigger group forms or, more prosaically, someone’s time is up and they have to go to work. Partings are generally unspoken but from time to time there’ll be a “thanks” or a “nice work”.

Another rule is: don’t jump red lights. The red-light jumpers aren’t “one of us”. They’ll be the commuter cyclists. Even though nearly all of us are going on to work afterwards, we are not commuter cyclists. Not for the duration of our Regent’s Park session, anyway. We occupy a separate realm. On one of the very rare occasions when I witnessed “one of us” jumping a red light, the offender got a telling-off from a fellow cyclist. The dream is of a clear round in which the five sets of lights – three of them pelican crossings – are all green. It rarely happens.

Regent’s Park is a kind of cycling utopia. It’s not like cycling anywhere else in London. But could that utopia spread? The future of London travel can only involve more cycling and less driving – or at least less driving by human beings, which itself must make cycling safer and more attractive. Project forward 10, 20, 50 years and only one scenario seems possible – a London turned into a fully-fledged cycling city.

Will Norman is London’s first full-time walking and cycling commissioner. He told me he found the idea of London as a playground for cyclists “interesting” – although he’s not in the job to endorse the city as one vast training circuit and I don’t think anyone thinks that would be a good idea. But if the city at large could learn something from the playful-but-serious atmosphere of the dawn park, it would improve fitness and quality of life in London enormously. “What I’m concerned about is the extent to which physical activity has been designed out of our daily lives,” Will Norman said, “so I’m looking for all kinds of ways to make walking and cycling more viable options for more people.”

In 2015 – the most recent year for which figures are available – there were 670,000 cycle journeys per day in London. That was a 100 per cent increase on 10 years previously, and a 200 per cent increase in the central London area. “Our goal is for every Londoner to live within 400 metres of a safe cycling route by the year 2041,” Norman said. Hardly a day seems to go by without the net closing a little tighter around car use in London, and another breakthrough in the expansion of cycling infrastructure.

On another October morning, I found myself in Lyric Square in Hammersmith, on a day when it was given over to pop-up street food outlets. The place was abuzz, but the pop-up where I lingered longest was one set up by TfL – part of the consultation process on the proposed Cycling Superhighway (CS9) that would transform the cycling experience between Chiswick and central London, which is currently pretty challenging. I chatted with a couple of TfL people. I admired the artist’s impressions of how it would all look. The sun was shining and the heart was gladdened.

The broadcaster Jeremy Vine is one of the country’s most high-profile cyclists, and as it happens, Chiswick is his manor. I asked him for his thoughts on the state of cycling in London. “London has some beautiful places to cycle – alongside Hyde Park, for example, is a great segregated track where I pootle along,” he told me. “But whenever I engage with motor vehicles on the roads – which I have to in Kensington, where uber-posh residents have insisted on keeping four lanes of traffic in their ghastly high street – I feel the threat. Cyclists won’t be safe until we have driverless cars. To me, it’s unbelievable that I can’t suggest that my 13-year-old daughter and I cycle from Chiswick to Trafalgar Square on a Saturday because it is simply too dangerous between Hammersmith and Hyde Park.”

We can all relate to that. I spoke to a number of Regent’s Park cyclists about their experiences and their hopes for the future of cycling in London. None of them was what you’d call a warrior. They appreciated what Regent’s Park had to offer. They recognised the progress being made with cycling infrastructure. But they were impatient for more, and faster.

My friend Lewis summed up our feelings: “The end of the combustion engine car is long overdue. When it happens, cars will inevitably be replaced by electric vehicles and, if driverless, presumably carefully monitored. That won’t turn London into a cycling playground, but it will be a base for a considerable uplift in civilised living. Bicycle riding of many varieties will flourish rather than be oppressed.”

In the meantime I feel Regent’s Park deserves to be protected – to be bestowed with some kind of special status. Area of Outstanding Natural Cycling? That would do.