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You will need to collect your luggage at LGW and then transport it over to LHR, and re-check it in there. Getting landside at LGW should be reasonably quick, 30 minutes or so. When you get to Healthrow Central you just follow the signs in the under passages to T3. It will probably feel a long way, but there are moving walkways for almost all the distance. You will probably have the boarding passes, so it's just the baggage drop. From check-in to security is very close, it's just upstairs. In normal circumstances you should have plenty of time for the transfer.