When is a garden bridge not a garden bridge? When it’s a bridge garden, according to Allies and Morrison, the Southwark-based architects who have come up with a cheap and cheerful alternative to the eye-wateringly expensive, contractually dubious proposal by Thomas Heatherwick and Joanna Lumley for a floating forest across the Thames.

Rather than spending £175m on installing two gargantuan copper-nickel plant pots in the middle of the river, in a public-private business model that could burden the taxpayer for years to come, they have realised we could simply plant some trees on a bridge that already exists. But which one?

Blackfriars bridge, which lands just a few hundred metres from the Allies and Morrison office, stretches up to 40 metres wide between its stately stone piers, carrying four lanes of traffic and a generous pavement on either side. With a bit of rejigging, the pavements could be consolidated into one 14 metre-wide, tree-planted park, while leaving enough room for cars, buses and a separated cycle lane.

By contrast, proposals for the garden bridge suggest bikes would be banned. The controversial crossing, whose campaigners have already spent almost £40m of its £60m public funding before construction has even started, would also be shut at night and closed several days a year for corporate events – part of a shaky business plan that also expects bridge users to donate £2 per crossing.

Large groups will be encouraged to register their visits in advance, phone signals will be tracked in a bid to deter protesters, while a list of draconian rules will prohibit playing musical instruments, flying kites and taking part in a “gathering of any kind”.

Freed from the burden of a huge debt and the demands of corporate sponsors, the Blackfriars bridge garden could be a truly public space. Constructed by engineer Joseph Cubitt in 1869, the structure has a built-in generosity emblematic of the days of Victorian civic pride. It already incorporates charming stone seating nooks above its five bastions, which would be incorporated into the park: “riverside alcoves for a sandwich at lunchtime, a break from a jog or a place for families to gather,” as the architects put it, “a garden for morning commuters as well as the quiet moments of urban life”.

The proposal is the latest, and perhaps the most feasible, in a series of alternatives to the costly vanity project, which was championed by Boris Johnson and remains supported by London’s new mayor Sadiq Khan, whose odd defence is that cancelling the scheme would cost twice as much as completing it.

It follows the satirical Folly for London competition, whose winner proposed constructing an eternal bonfire on the Thames. Fuelled by trees felled from London’s parks, usefully freeing up land for private development, it would be “an eternal flame dedicated to 21st-century planning departments and developers”.

Other entries to the contest included a “Scrotopolis” of bulging pink scrota and the Jesus bridge, an invisible crossing that would allow commuters to walk on water – a dream as probable as the idea that Heatherwick’s scheme could ever get this far.