The winning team - which will design the residential project in Bedfordshire - saw off Ash Sakula, Fraser Brown MacKenna, C F Møller, Riches Hawley Mikhail and Sarah Wigglesworth to bag the scheme.
The competition attracted 63 expressions of interest from architectural practices across the UK, Europe and Africa.
The £15 million project is being developed as a partnership between Aldwyck Housing Association, South Bedfordshire District Council, Luton Borough Council and the Housing Corporation.
In a statement, the jury said the Proctor and Matthews/Mae team had produced a scheme which delivered the densities required 'without appearing crowded', and with a mix of housing typologies that would result in a development with a sustainable neighbourhood rather than an 'estate feel'.
The jury was also impressed by the winning team's considerable experience of using prefabrication in their previous housing projects.