Taxis etc
Addison Lee offer a service from the airport to London.
There is also an official taxi service called Airport Cars Gatwick which you can pre-book for: https://www.airportcars-gatwick.com/
Prices will vary and it will be a convenient door-to-door service.
We have never used either of these services for this journey so cannot comment. But they are there. Make sure you book in advance, and tell the company your flight number so they can monitor any delays.