The Bold Home studios were set to be affordable self-build spaces for the creative community, costing £100 a month before bills.
Occupants were to be provided with the infrastructure and materials to construct their own spaces in the first six levels of the car park, which would be transformed into a "colourful artists' favela".
Bold Home was established by Second Home founder Rohan Silva, entrepreneur Sam Aldenton and Bold Tendencies founder Hannah Berry, who has been running an arts programme in the Peckham car park for the last nine years.
"With so many artist studios in Southwark and across the city having disappeared over the past decade – and the remaining 30 per cent forecast to disappear in the next five years – this is a terrible result for London," said the trio in a statement.
Bold Home's proposal would have seen the company invest £3 million in construction to overhaul the car park, as well as pay annual rent of £200,000 to Southwark Council.
The scheme was designed by Spanish architects SelgasCano, who created this year's Serpentine Gallery Pavilion as well as Second Home's co-working space in London.
The proposal had received public support from Serpentine Gallery directors Hans Ulrich Obrist and Julia Peyton-Jones, who described it as "exactly the type of farsighted and urgent initiative that London needs".
The Institute of Contemporary Arts director Gregory Muir also highlighted the need for new workspaces.
"London is now cooling at the level of artistic production owing to a sharp decline in artists' studio provision," he commented. "Without spaces in which to work, artists can't make things. They can't test their ideas or evolve their practice."
London mayor Boris Johnson attempted to address the issue of ever-decreasing studio space by publishing an A-Z of planning and culture, which urged developers to prioritise culture as well as housing.
The document issued by his office offered steps that could be taken to protect and support culture, and revealed that London is set to lose 3,500 creative workspaces by 2020.
"The big issue is affordable spaces for creative people – especially artists," Silva told Dezeen. "Over the past decade we've seen a slow decimation of studios across London, and we have to fight back."
"It's never been more urgent and the need has never been greater," added Aldenton.
"We were excited when Southwark Council invited bids for what to do with the car-park space, which is a key venue in Peckham. We felt [it] had enormous potential to deliver jobs, space and creativity for artists and local people."
London designers Barber and Osgerby have also warned that the city is at risk of losing its status as a creative capital.
"It's becoming more and more expensive," added Barber. "I have a horrible feeling that's going to have a detrimental effect in the near future on more young creatives."