I was told at a meeting several years ago that BA would not tolerate low cost airlines operating at BHX or MAN and the airports were advised by BA to disincentivise low cost operations or they would be reviewing their own position at these airports.
Very political, and FR only opened bases once BA had disappeared and I would guess that Easyjet had better things to do with their fleet than going back to BHX having been politely declined in the past. Easyjet were picking up the pieces of GB Airways at Manchester but had no similar obligation to operate out of Birmingham.
My source at the meeting was the commercial director of a BHX based airline so I trusted that he knew the politics of the day.