BA are very dominant at T4. By moving some services to other terminals, they are still dominant at T4 but they increase their presence at the others.
I believe the management of the terminals is partly controlled by an “airline council” consisting of the carriers using that terminal. By having a greater voice in T3, BA can try to move things in their direction.
Just a hunch, but I guess that when T5 is ready BA will abandon T4. They will move a lot to T5, but also T3.