The concrete building currently hosts the famous rooftop bar Frank’s Café, along with a cinema on the lower floors.
Both will continue to operate, with the new scheme transforming the intermediate levels into a new creative community for local artists and entrepreneurs.
Turner told the Architects’ Journal: ‘The council is starting to take a strategic approach to Peckham, and is appointing a lot of smaller and younger practices to help regenerate the area. This project is part of that.’
He said that the practice would be transplanting a number of ideas from its successful Pop Brixton scheme, which has created space for a similar community using shipping containers.
The Peckham scheme will also create a gallery, performance and events space alongside small retail space and food units for independent traders.
As in Brixton, tenancies will be prioritised for local residents and businesses as well as those offering training opportunities for local youngsters.
The team is planning to work with local people to develop the scheme’s design through a public consultation process.
Turner added: ‘The car park has created an amazing platform for the arts during the summer months in Peckham, and our proposals seek to carve out spaces within the redundant middle floors of the building to extend these possibilities year round, while simultaneously providing a huge amount of much needed new creative workspace for Peckham’.