Thameslink CityFlier is the fastest route between the City and the Gatwick
airport. It runs from Bedford to Luton Airport. Depending on what Terminal
at Gatwick you're flying from it's about a 10 min. walk to South Terminal
and 15 min. to the north - although I did it much faster than that. There
are about 4 trains an hour. It takes about 45 min. - stops at London Bridge,
Blackfriars &Farrington. Thameslink has it's own platform at Gatwick (No.
4 I think) and you just follow the signs. When you get off at the King's
Cross Thameslink station you just cross the road to get to the King's
Cross underground and the underground goes direct to Heathrow. You can
get an Interchange ticket with the underground but can't tell you how
that works. They quote a price of 9.50 pounds (2000 rates)single from
King's Cross to Gatwick. As with all U.K. railways the further in advance
you book the cheaper it is.
Check out http://www.thameslink.co.uk