I am travelling from the Caribbean to Geneva via London . Arrival Gatwick 9 am. Departure heathrow at 2 pm. With such a tight window to traverse and change airports I need to know from now whether my luggage will be forwarded directly to Geneva or whether it has to be collected at Gatwick first. Traveling on British Airways and both flights were booked at the same time. Please respond only if the answer is known with certainty. Such knowledgable assistance would be very much appreciated.