Dunno. There are still only a limited number of LHR slots available, so it all depends upon what happens with regard to AA/BA finally being approved.
If they're finally able to start codewhoring on each other's North Atlantic services, it's possible that some frequency adjustments could be made in markets where they have a shared presence, i.e. LHR-JFK where AA has six flights and BA has eight, and LHR-ORD where AA has five flights and BA has three.
That in turn could free up slots for AA to move its three flights a day from DFW and RDU over to LHR, and for BA to move its DFW, IAH, MCO, TPA and ATL flights over to LHR.
The downside to that is that BA has built up a decent connecting hub at LGW, especially to Africa, and I don't know that they want to write off the North America feed so quickly.
For reference, in the 6/1/07 schedule:
LHR to: JFK 6X, ORD 5X, BOS 2x, LAX 2X, and MIA 1X.
LGW to: DFW 2X, RDU 1X
BA:
LHR to: JFK 8X, ORD 3X, BOS 3X, LAX 3X, SFO 2X, SEA 1X, PHL 2X, IAD 3X, BWI 1X, EWR 3X, MIA 2X, PHX 1X, DEN 1X, DTW 1X
LGW to: IAH 2X, DFW 1X, MCO 1X, TPA 1X, ATL 1X
I might have missed a few along the way...