The design involves dividing the main shopping centre in the area into three smaller venues.
The design team is working for Choices for Graham Park, a joint venture between registered social landlords Notting Hill and Genesis. Developer Countryside Properties has an advisory role.
The team's application is expected to go to the council's planning committee next month.
A decision on the scheme is expected by September.
Levitt Bernstein is also the designer of Bermondsey Spa, a scheme for 605 homes in Southwark, south London. This will accommodate a mixture of tenures and incorporate a supermarket, health centre, commercial space and "community use" space.