A diesel-powered compressor was destroyed by the flames.
Station Manager Joe Kenny said: “The compressor was in an open area on the first floor, close to an unfinished section of the building.
“If firefighters hadn’t acted fast it could have spread very quickly along exposed timbers and into the building under construction, but thankfully it was brought under control at an early stage.”
Four fire engines and 21 firefighters and officers from Greenwich, East Greenwich and Plumstead attended the incident.
The Brigade was called at 1500 and the fire was under control at 1556.