Is 4 hours a reasonable connection time to transit between LGW and LHR? I have actually found award space in CW for the 4 of us from TPA-LGW-transit-LHR-ORY/CDG and back the same route in June 2016.

With 4 of us, would it be best to hire a car or just take the shuttle?

Also, assuming it's all on 1 BA itinerary will BA will have to accommodate us if there's a problem?