The first Gatwick Express to Victoria station leaves at 4:35.  The first National Express bus to Victoria Coach station leaves at 4:40 (north terminal) and 4:55 (south terminal).   There’s a “first capital” train to London Bridge at 3:05.  Try this link: http://www.londontoo…

Southern runs services at 0305 and 0400 monday-saturday from gatwick to victoria. On sunday they run at 0315 and 0415. First capital runs a service at 0335 up the the north-south line calling at blackfrairs and kings cross thameslink. Where in central london are you trying to reach?
cheers
howie
Ps.Here’s the timetable for southern services
http://www.southernr…

If you decide none of these options will work, for sure use a prebooked car service instead of a cab. From what I’ve read, that will save a fair bit of money. An example of a car service that many people use happily is Just Airports. I should say that I’ve never used one, so can’t comment personally – just repeating what I’ve read over and over.

Another thing is that just because your flight is supposed to land at 2:30 AM does not mean it necessarily will. At that time of night, the odds are on you landing early and speeding through immigration in a snap, but I would keep in mind options from 2 AM onwards when you are making plans, as you could be either early or late.

Thank you everyone, for all this great info.  You’ve definitely given me a few options. 

Thanks again!