The firm set-up three years ago by former Barratt London regional chairman Adam Lawrence, has exchanged on a former office building in Eastcote village in the London Borough of Hillingdon.
The site has planning permission for a £15m residential scheme – a collection of 42 one, two and three bedroom apartments.
Work will start in September this year and the development is expected to be complete in early 2015.
Brian Betsy, Managing Director at London Square, said: “There is a very buoyant local sales market in suburban north-west London at the moment, which we have experienced first-hand at our Ruislip development where we have sold 70% of the scheme off-plan since the end of January.
“Buying this site with planning permission will allow us to start work as soon as possible and capitalise on the strong demand.”