Layover in London

Hi All,
I'll be moving to Toulouse this October, and my flight has a 13 hour layover in London.  My plan is instead of wasting time in the airport, I'd like to see as much of London as I can (and I'm really excited and an early planner so I'm already thinking about it :)). 

If anyone can give me advice on the best way from the airport to the city center (preferably train if possible), and maybe even some suggestions on things to do/places to eat I'd really appreciate it!

Cheers,
Roxanne

Assuming your coming into Heathrow airport, you can get the tube (Underground\metro) into the heart of London.
What time do you land your departure time? Would be helpful to give some tips on sightseeing etc.

Thanks for the reply! I land at 6:55am and leave again at 8 or 9. So may be a 14 layover.