If you do have to transit between LGW and LHR, an option that is more expensive, but not prone to traffic delays, is to use the express train services. The Gatwick Express will take you between Gatwick and Victoria train stations in 30 minutes. You would then use the Tube to connect from Victoria to Paddington. At Paddington, you hop the Heathrow Express which is about a 15-20 minute ride to Heathrow, depending on your terminal.