Among the more amusing frauds of the energy company Enron was the time, in 1998, when it decided to create an entire fake trading floor at its Texas HQ – complete with TVs, computers, and shirtsleeved guys shouting down phones – to fool Wall Street analysts visiting for its annual general meeting.

Now, however, the mayor of London, Sadiq Khan, appears to be aiming for something even more ambitious – an entire fake cycle network. I am in south-west London, in an alley about six feet wide, wedged between a railway line and the back garden fences of Southdown Road. According to Khan, this is the Wimbledon to Raynes Park Quietway, part of the 140km of cycle infrastructure, which he claims to have built since taking office.

There isn’t room for two bikes to pass safely. The cracked, bumpy tarmac hasn’t been touched in years. The crossing of the busy Lower Downs Road lacks even a dropped kerb and throws you blind into traffic emerging from a long, tunnel-like bridge under the railway. No work at all, not even new signposting, has been done here.

Nearly three years into his term, stung by criticism that he has achieved almost nothing on cycling, Khan has upped the pace – not of construction, alas, but of publicity. Few weeks pass without the mayor or his staff hailing his terrific progress on all fronts. But when you dig into these claims, they are false.

Khan and his social media accounts have repeatedly claimed he has doubled cycling spend to £169m a year. In December his walking and cycling commissioner, Will Norman, said Khan was further increasing this to an average of £214m a year. Spending in the last full year, 2017-18, was in fact £90m. Spending in 2018-19 is projected to be £86m. Even these amounts are puzzling, since outside three autonomous “mini-Holland” London boroughs, almost nothing meaningful has been delivered.

Wimbledon to Raynes Park is one of more than 50 sections of Quietway backstreets route, totalling about 100km, which Khan claimed to have built and to be complete in a list he gave to the London Assembly in November. The term “built,” he admitted, can mean as little as putting up signs – or, often, replacing old signs with new ones.

Over the 10 weeks since the list was published, I’ve ridden most of the sections of route which Khan claims to have built. In a few places, I found, new Quietway signs have indeed been painted on the road, though they are often hard to see under the queues of vans and rat-running cars. The last thing many of these routes are is quiet.

Elsewhere, I discovered that City Hall has taken decades-old traffic-free cycle routes, such as the Thames towpath and the Greenway in east London, put Quietway signs on them and claimed them as new routes. This alone accounts for 26km of the 100km that has supposedly been delivered. In other places, there were traces of work begun but not finished.

At least a further 30km consists of little more than rebranding existing, unsegregated, noughties-era London Cycle Network (LCN) routes on sometimes busy and congested streets. Khan claimed in a press release that “Quietways are leading to a big increase in cycling, with 24,000 bike journeys on Quietway 2 within its first week of opening.” Most of Quietway 2, under its former name of LCN route 8, has in fact been open for more than 10 years, which explains why 24,000 journeys a week are made on it.

But on very long stretches of the network claimed to be complete, and even by Khan’s minimalist definition, I found nothing: neither new signage nor any trace of work starting. (Khan last month issued a revised Assembly answer, still claiming that all the sections concerned had been constructed but admitting that wayfinding was still awaited on most of them.)

The Quietway programme is a scandal. Khan has spent at least £46m on the Quietways since taking office. That money has bought not a single meaningful route that did not already exist (the only proper new route, Quietway 1, was built under Khan’s predecessor, Boris Johnson, for whom I was cycling commissioner) and very little else of any real value to cyclists.

There is a useful, albeit part-time, new link at the Thames Barrier, which cuts out a long diversion. There are several new road crossings, though often not very good ones – the sort that force you to cycle up on to the pavement, double back on yourself and weave around pedestrians. The Greenway and part of the River Wandle trail in Wandsworth have new lighting.

In the borough of Southwark, three roads have been closed to through traffic. But across the whole of Greater London, that is more or less it. Nearly £50m is an astonishing amount to pay for such meagre returns. Unsurprisingly, even where painting signs on roads has actually been carried out, it has done little to encourage cycling. I stood beside Quietway 6 in Manor Park one evening rush hour. In 30 minutes, I saw four cyclists.

The other 40km or so of infrastructure which Khan claims to have delivered is protected cycle lanes. Again, this claim mystifies observers. Since May 2016 the mayor has started work on only 4km of protected superhighway route (8km if you count lanes in each direction), all of them schemes consulted on and left to him by the previous administration. In an Assembly answer, he inflated his total by including several schemes – through Hyde Park, for instance – where building in fact began before he took office.

The three mini-Holland boroughs have done a further 14km or so of protected route – almost all of them schemes consulted on and agreed under Johnson and where building often also began before Sadiq took office. Khan pays for the mini-Hollands, but has no role in delivering them; all the hard work was done by the councils concerned.

Khan must share blame for the fiasco with the London boroughs, who own nearly all the side streets on which the Quietways run and most of whom have resisted meaningful change on their roads. For this reason I have long said that the Quietway programme should have been cancelled, with the money redirected to superhighway routes on main roads and the handful of willing boroughs. But, as with Crossrail, the mayor has made things worse for himself by refusing to face up to problems when they arise, then by making claims of success he can’t back up.

Asked for a response to these findings, Norman repeated the 140km figure and claimed that “under [Khan], new high-quality cycle infrastructure is being delivered all across London.” But, perhaps to prevent people doing the sums, City Hall plans a further rebranding, dropping the superhighway, mini-Holland and Quietway names altogether; those LCN routes will soon be getting their third set of new signs. In the press release for his “cycling action plan” in December, Khan claimed he would ensure that all his new cycleways meet strict new quality standards. But the plan itself makes clear that the standards are only aims and aspirations.

The action plan is, by my count, Khan’s fourth glossy document making big promises on cycling. Actual action is more elusive. The mileage of meaningful new route proposed and built by the mayor remains at nil, though there has recently been yet another pledge that work on something worth having will finally start in the summer. Perhaps if we piled up copies of all the action plans in the roads we could create some of the protected space for cycling London so desperately needs – at least until the next time it rains.

• Andrew Gilligan was London’s cycling commissioner from 2013-16