brs planespotter,
I remember hearing from many Airbus pilots including a trainer I personally know, and they switch Engine 1 off before entering stand so they can get the air bridge or in EasyJets favourite case the Stairs
and engine 2 is switched off as soon as parking brakes are applied along with the Anti-Collision lights switched off, so a short turn around can be completed. Also I noticed BA do the same thing with there aircraft, becuase the pilot switched the left engine off and came into stand and then had to put a lot of power on the right engine (lots of vibration) to get onto gate correctly.