I did check national express (www.nationalexpress.co.uk) but all their Services to London run via Brighton!
Apart from Gatwick express, Southern and Thameslink run services to London. It is quite confsing and you should buy a ticket for the train operator you wish to use.
Gatwick Express and Southern run to Victoria. Southern and Thameslink run services to London Bridge. Thameslink runs through central London

http://www.gatwickairport.com/