The station takes its name from Stamford Brook, a tributary of the River Thames that is now predominantly underground.

The Piccadilly line uses the inside tracks, but does not stop here except in the westbound direction on rare occasions The line through Stamford Brook station was opened on 1 January 1869 by the London and South Western Railway (L&SWR) on a new branch line to Richmond from the West London Joint Railway starting north of Addison Road station (now Kensington (Olympia)).

In the early 1930s, the London Electric Railway, precursor of the London Underground and owner of the District and Piccadilly lines, began the reconstruction of the tracks between Hammersmith and Acton Town to enable the Piccadilly line to be extended from Hammersmith to Uxbridge and Hounslow West (then the terminus of what is now the Heathrow branch).

Services on the Piccadilly line began running through Stamford Brook on 4 July 1932.

Originally, the station had an island platform with District line trains serving one side in each direction.