Is it possible to start the engines while on push back? I was recently on a flight and the the engines started after push back has been initiated. I was always under the impression that the process required a GAU to feed pressurised air or use of the APU. 
But the APU wouldn't be used at a major London airport when ground services are available?

How did they start then?
Aircraft engines are started using the APU or a Airstart Cart. The GPU is for electrical power only and the engines are started off air power. It may be a Airstart was not available or they were running late on the block time and they blocked  using the APU to start the engines to make the block time. After engine start and before takeoff the crew will shut down the APU. Most US airlines start their engine off APU air unless the APU is not working then they will start off a Airstart Cart.