The project - for a private client - is a substantial remodelling of a 1960s house in the West Greenwich Conservation Area.
The practice has obtained permission to add a third storey and will rework the elevations completely in brickwork - replacing the shiplap between the windows with brick sourced to match the original.
The original design for the project faced considerable opposition from locals and conservation groups, and was refused planning in February.
The amended, and now approved, application is 1m shorter and has the backing of the Greenwich Conservation group and the Greenwich Society.
D'Avoine said: 'A metre in that context barely makes a difference and the ambition now is to build it beautifully.'
Work on the 20-week programme is due to start on site by the end of the year.