JoAnn we flew through LHR going and through LGW on the way back, connection was to/from BA - fortunately no luggage problems for us. On the way home from Geneva we flew through LGW - at check in BA put a "fast LGW transfer" tag or, something like that, on our bags so they would get noticed. Seemed to work.
I would cross pack and carry on a few days worth of stuff which will go a long way towards minimizing the problem if you have one.
