We are invited to embark on an adventure. It will be an emblem of the enterprise of a proud people. Its cost will be zero, or not much, or a sum that, if quite large, will absolutely be worth it. Naysayers are pooh-poohed. Practical objections are for losers. A deadline is imposed, meaning we have to rush ahead with it at all costs. And driving it all forward are the quipping, gurning, dissembling features of Boris Johnson.

For Brexit, read the garden bridge, an earlier vanity project promoted by the former mayor of London and foreign secretary. For it was Johnson who picked up the charming-sounding idea, conceived by Joanna Lumley, of building a flower-filled crossing from London’s South Bank to the Temple. For whatever selfless or selfish reasons (you decide), he chose to throw his mayoral power behind it, steamroller objection and commit public money to an architectural unicorn.

An itemised bill for its failure has just arrived: £53m in total, of which £2.76m (including VAT) went to the designer Thomas Heatherwick; £12.7m to the engineers Arup; £2.3m to lawyers; and £1.7m went on the salaries of the executives who didn’t in the end execute the project. It cost £1.3m to survey the riverbed and look for unexploded wartime bombs. The project’s adequate but unexceptional website cost £161,000.

The largest sum for this great patriotic endeavour – £21.4m – went to the suspiciously foreign-sounding joint venture of Bouygues Travaux Publics and Cimolai SpA, which won the tender to build the bridge in 2016. They had to be paid for their costs in gearing up for the works and then winding down. They were appointed despite substantial doubts about the viability of the project, at a time when neither the funds nor all the permissions needed were in place. One argument for doing so was that the bridge had to be built quickly, so as not to get in the way of the Thames Tideway tunnel, the giant sewer being constructed in the river.

It’s like that moment in a fancy restaurant when all those little extras – the olives, the sourdough bread, the water, that dessert wine about which the sommelier was so persuasive – add up to more than you thought. And your smiling host, who you thought was going to pay, has left his wallet at home. The taxpayers of Britain and of London, via the Department for Transport and TfL, have to pay £43m of the total. When the bridge was announced in 2013, it was going to be free to the public, entirely funded by private sponsorship. “A gift to the people of London”, it was called.

Joanna Lumley at the site of the proposed garden bridge across the Thames. Photograph: Philip Toscano/PA

Along the way, as Margaret Hodge detailed in a 2017 report, rules were bent and arms were twisted. The competition that chose Heatherwick and Arup seemed to be heavily loaded in their favour. Both the budget and the likely public contribution kept on going up, for the running costs as well as for construction. Flagrant conflicts of interest were ignored. Requirements were set for the Garden Bridge Trust, the charity in charge of the project, to prove its viability but then relaxed and waived. Public money was given to the trust despite its failure to meet some conditions previously set by TfL.

Some media outlets, including the Observer and the Architects’ Journal, consistently pointed out the flaws in the trust’s case – its over-optimistic view of both fundraising and costs, for example – for which we were rubbished by supporters of the bridge. Johnson claimed, without evidence, that the AJ’s determined and methodical reporter Will Hurst was motivated by personal dislike of Heatherwick.

The project was cancelled in 2017 by Sadiq Khan, Johnson’s successor as London mayor, on the reasonable grounds that the trust seemed unlikely to fill a £70m funding gap. What remains is a loss of public money on a scale with that spent on the Kids Company charity, with the difference that the latter achieved at least some of its objectives. It is, in other words, a scandal. If we weren’t so distracted by that other Johnson-generated fiasco, Brexit, it should be at the centre of attention. The Charity Commission must certainly investigate the trust’s board for its role in the project. (Trustees included Lord Mervyn Davies, Roland Rudd, chairman of Finsbury, and Clare Foges, former chief speech writer for David Cameron.) Lumley, also somewhat tarnished by her performance presenting the Baftas, will have to work hard to rebuild her image as a national treasure.

But the chief culprit is Johnson. As mayor, he was ultimately in charge of TfL and it’s clear from the Hodge report that he leaned heavily on officials lower down the hierarchy, who then had to find ingenious and questionable ways to fulfil his will. He chose to own it and he should own the consequences. Before the project was publicly announced, Johnson flew to San Francisco, to try to persuade Apple to pay the full cost of what he was offering to call the Apple bridge. We should be thankful that this exercise in branding the Thames got a dusty response. (What next: the Google Stonehenge, the Facebook Snowdonia?) But this story brings us back to another parallel with the Brexit fantasy, in this case the belief that global corporate giants will be gagging to seize the magnificent opportunities we offer them.

The Brexit lies are now familiar enough: the one on the bus about the NHS; the one that the deal would be easy; that the Irish border wouldn’t be a problem; that hard Brexit is the will of the people. But they were all prefigured by the dishonest handling of the bridge. The question is: why on earth should anyone believe any promise or statement that this man makes, about anything, ever again?

• Rowan Moore is the Observer architecture correspondent