The overhaul of a Modernist 1950s school for girls in London by Allford Hall Monaghan Morris has won the RIBA Stirling Prize 2015 for the biggest contribution to British architecture in the last year (+ slideshow).

London-based Allford Hall Monaghan Morris (AHMM) added six new buildings to the Burntwood School campus in Wandsworth, among a number of retained historic structures including two designed by the late English architect Leslie Martin.

The aim was to create a "complete and coherent campus", featuring new teaching facilities, as well as modern sports and performing arts facilities, interspersed with numerous lawns and public squares.

The project was named winner of the Stirling Prize in a ceremony this evening at the Royal Institute of British Architects (RIBA) in London. It was selected ahead of five other shortlisted projects, including a Maggie's cancer-care centre in Scotland by Reiach and Hall Architects and MUMA's expansion of Manchester's Whitworth Gallery.

The judges – which included RIBA president Jane Duncan, and architects Steve Tompkins and Peter Clegg – praised the building for being the "most accomplished" project in the running.

"Burntwood School demonstrates the full range of the skills that architects can offer to society," they said. "It encompasses great contemporary design and clever reuse of existing buildings as well as superb integration of artwork, landscaping and engineering."

They also applauded the "technically sophisticated" use of prefabricated modular structures, which relate to "sculptural" facades where precast concrete panels create angled recesses around windows.

"Burntwood sets a standard in school design that every child in Britain deserves. It is a culmination of many years of creative toil by Allford Hall Monaghan Morris in designing schools up and down the country. This is their masterpiece," they added.

This is the first time AHMM has won the Stirling Prize. But the firm has been shortlisted three times before – for Westminster Academy in 2008, Kentish Town Health Centre in 2009, and the Angel Building in 2011.

The last time a school was awarded the prize was in 2011, when Zaha Hadid's Evelyn Grace Academy was named winner.

"Good school design makes a difference to the way students value themselves and their education, and we hope that Burntwood winning the RIBA Stirling Prize shows that this is worth investing in," said AHMM director Paul Monaghan.

"Schools can and should be more than just practical, functional buildings – they need to elevate the aspirations of children, teachers and the wider community."

Other projects shortlisted this year were the NEO Bankside housing by Rogers Stirk Harbour + Partners, a campus building for the University of Greenwich by Heneghan Peng Architects and a Peabody housing development by Niall McLaughlin.

RIBA President Jane Duncan commented: "Burntwood School shows us how superb school design can be at the heart of raising our children's educational enjoyment and achievement. Allford Hall Monaghan Morris, experienced school architects, have created a stunning campus. They have produced delightful, resourceful and energy efficient buildings that will benefit the whole community in the long term."

Last year's winner was Haworth Tompkins' new home for the Everyman Theatre in Liverpool.

Photography is by Timothy Soar.