The scheme - which is for an extremely cramped site currently occupied by a low-rise warehouse - has taken more than a year to work its way through the appeals process.
The project will be mixed-use due to planners' demands that the site retains its employment status. It is surrounded on all sides by Georgian buildings.
The development includes ground floor office accommodation with nine residential apartments above and nine basement parking spaces.
The scheme was shortlisted for the London Architecture Biennale 'Urban Interventions' Exhibition in June 2004.