When Boris Johnson eventually stops being mayor of London, whether en route to becoming Tory leader or prime minister, what built legacy will he leave to the capital? He'll point, no doubt, to the likes of the "Boris bikes", the London Overground extensions, the Olympic village or the Shard. This would be dishonest, as each of these for better or worse were Livingstone-era projects he happened to inherit.

In terms of real built things, he can only really point to two large-scale structures which owe their existence to his rule. The ArcelorMittal Orbit, the egregious sculpture/observation tower that looks over much of east London; and the Emirates Air Line, a cable car also in the east of the city. What links the two is a peculiar form of overbearing whimsy and equally overbearing sponsorship. That corporate cash was supposed to obviate the need for actual public investment and public control, free money that would mean no unpleasant taxes. So why has Johnson asked the European Union for £8m to bail out his cable car?

The cable car, Air Line or "dangleway", as some have more appropriately called it, is ostensibly more useful than Anish Kapoor and Cecil Balmond's hot pink entrail in Stratford. It was certainly sold as such. It was built on the almost complete New Labour tabula rasa of the Greenwich peninsula, next to the ex-Millennium Dome-now-O2, the Canary Wharf commuterville of the Millennium Village, and a hangar that once housed the David Beckham football academy.

This post-industrial area was once earmarked in the late 1990s as a mini-ecotown with a nature reserve and its own tube stop, a sustainable, car-curbing model for the future. It has long since become a mess of car parks, retail parks and US-style enormodome exurban entertainment. The cable car was to connect this with the not entirely dissimilar landscape on the other side of the Thames, at the former Royal Docks, a space marked by hundreds of luxury flats and the ExCel exhibition centre.

In theory, maybe, this could have been sold as a return to the development's original principles. Rather than driving through the hellish congestion of the nearby Blackwall Tunnel, south-east London commuters could get to work at Canary Wharf or ExCel via a "state-of-the-art" cable car, and get an incredible view into the bargain.

Accordingly, it was treated as a piece of public transport infrastructure rather than a piece of theme park whimsy like the public walkway over the O2 that opened at the same time. It was even added to the tube map. However, there was one overwhelming problem with the idea. The Jubilee line, just next door, could take you on exactly the same journey – North Greenwich to Canning Town – in two minutes. For half as much money.

Had Johnson or any of his team lived in southeast London, they would have been aware of this obvious fact. So, although it was used by tourists during the Olympics, it has since lost money at an astonishing rate – £50,000 a week, in fact. It's estimated that only around 16 people regularly use it to commute. Despite part of the money being put up by the United Arab Emirates' national airline (who got a mention on every tube map in London for their pains), it was still a total financial failure, hence the begging to the EU.

What is especially telling about the dangleway and its ignominious failure is that southeast London has long been in need of real infrastructure and investment. DLR and Overground extensions have made up some ground, but mostly southeast Londoners rely (like the rest of the country, but unlike those north of the river) on a massively unreliable and slow train network. River crossings are especially tricky. Among the first things cancelled by Johnson on coming to office were the Thames Gateway bridge, a DLR extension to Dagenham and a cross-river tram. Such things were evidently utopian – by now, the big infrastructural idea, depressingly supported by Labour councils, is an extension of the Blackwall Tunnel.

Worthless as it may be as an alleged piece of public transport, the dangleway is more useful as an image of the sort of London the mayor has created. The GLA under Livingstone was a tragedy, a worthy attempt at a 21st-century GLC that became a paradise for developers and financiers. But since 2008, London has been run as a twee austerity nostalgia theme park, with an almost ostentatiously negligent attention to the city's problems. Worst of all, it doesn't even work on its own terms, as we now find a mayor addicted to allegedly cheap, corporate-sponsored stunts suddenly, if unsurprisingly, turning to public money to bail them out.