Last time we had to travel from Gatwick to Kensington (Olympia) and the best way was to change at East Croydon. We discovered that Gatwick to East Croydon was only about 3GBP (off peak) and that we could save money for the minor inconvenience (given we had to change there anyway) of exiting the station and re-entering using a different credit card . As we didn’t go through zone 1, the fare was then only 2GBP. So 5 GBP for the total journey. Much less expensive than expected.
But to get to Central London it would be 8GBP using this method, but obviously more inconvenient if not already needing to change at East Croydon.