It is possible to transfer bases, but you can only transfer bases once you have completed your probationary period and if 1) there is a vacancy at the base you want to go to and 2) if the base you are wanting to leave can afford to lose you.
So, it's really a case of how long is a piece of string for how long it will take to get to the base of your choice. London bases are always desperate for staff, therefore it is harder to get out of them than in.
I am not sure of how many people are based in EMA though, perhaps an EMA member can answer that?