Apex Airspace specialises in putting prefabricated housing modules on top of existing buildings to provide an upwards extension.
Subject to planning, the £8m Southwark scheme is expected to be built in just 45 weeks, from design to completion.
The intention is to add one storey to a block of flats, providing 11 affordable rental flats to LSHA at no cost and 17 for Apex Airspace to sell.
In addition to the 28 new flats, Apex will renovate the existing building and provide a new lift for the whole block.
The location of the tower block to be extended was not disclosed.
Arshad Bhatti, managing director of Apex Airspace, said: “We are delighted to be working with Lambeth & Southwark Housing Association to address the shortage of affordable new homes in London. LSHA has a rich heritage in the provision of affordable housing, but they are also at the forefront of innovative approaches to housing solutions.
“Airspace offers the opportunity to unlock value from the unused airspace above properties – value which is otherwise unused. We hope that this will be the first of many such partnerships.”
LSHA chief executive Mark Jackson said: “We are very excited to be partnering with Apex Airspace. The opportunity to utilise our existing assets for new affordable housing at no cost to the housing association, whilst also reducing our maintenance spend, was one not to be missed. The Apex Airspace offering is a unique and compelling one, and we look forward to progressing on this first joint project together.”