I believe that in the recent revised deal that easyJet signed with LGW included a commitment that all operations could be handles under 1 roof at North. I may be wrong but I recall that this was to be achieved over a 3 year period. May stand corrected.
Would be surprised if BA would move to South, given the focus on improving the North Terminal in recent years, including the opening of a new check in area etc.
It could make some sense in having BA and EZY at North and all other operators at South.