Ken Shuttleworth's practice wants to create 273 luxury new homes and 33,000m2 of office space on the 1.2ha site north of Soho.
Make has worked alongside high-end development firm and interior designer Candy and Candy on the planning application, which was submitted to the City of Westminster on Friday.
Make project architect Simon Bowden said: 'The existing buildings resemble a fortress and we propose to open the site outwards to the surrounding streetscape.'
He added: 'Our scheme will create the first public garden in this area of London, which will also form a fantastic setting for the wonderful chapel.
'The new buildings will be respectful of their context, but bold and contemporary in their execution, creating a world-class development which will greatly enhance this part of the West End.'
If planning permission is granted, it is hoped that the demolition of the existing buildings could start before the end of the year.
The first new tenants are expected to start moving in during 2010.