The three-bedroom house measures only 2.8m in width, and will be built on a 'left-over' sliver of derelict land.
The practice claims the project is an 'experiment aimed at creating habitable conditions from an awkward urban site'.
The scheme was the centre of an ongoing spat between the practice and Southwark Council's planning department. The development went to an appeal, with an inspector eventually giving it the green light after two years.
Slotted into this narrow space between buildings, the scheme is called 'Toast House, bacuse it resembles a 'three-storey slice of toast'.
The ground floor houses a master suite with an entrance lobby. Two single bedrooms are located on the first floor, with the top floor accommodating the kitchen, with balconies at both ends.
In order to limit the space taken up by external walls, the structure is timber-framed with insulation between the studs.
It is hoped the £60,000 house will start on site in early 2007.