Is the flight to AMS the last flight on the ticket (i.e. no return legs)?

You could consider just booking a one-way LHR to AMS and taking that instead of heading to Gatwick. That only works if the AMS leg is the very last part of the ticket. Could look at RFS in which case it will cost less cash than the transfer price to Gatwick probably.

Note that if you do this (or if you transfer to LGW) you have to collect any checked bags and clear immigration.