I always understood it as being due to political reasons within football.
FIFA has always had a problem with the power within the game of Britain as a ‘commonwealth’ (not THE Commonwealth). It is a unique situation in that one State, has four separate footballing countries (and therefore, four votes within FIFA).
It’s also, one of the (admittedly, myriad) reasons, why Britain has never sought to have a national side, representative of the state, university unless in ‘one-off’ situations, such as the 2012 olympics.
I could well be incorrect on this, it isn’t something I’ve done a good deal of research on, though I remember reading about it from different, serious sources, throughout the years. It also appears to be the exact type of petty squabble that FIFA, and the Home associations seem to relish.