I live in Surrey and Thorpe Park And Chessington World of Adventures are very close by.
Chessington is a 10 minute walk from a railway station
Chessington Directions
Thorpe Park run a shuttle bus from the nearest station
Thorpe Park Directions
Alton Towers is about a 3 hour drive - I don't know about public transport. I've never done this as a day trip from Surrey - I always stay with family who are only an hour or so away from AT.
All are run by the same company and are a good day out. Thorpe Park is has a reputation for being for teenagers and adults (although it also has kiddie rides) and Chessington is more for families (but my teenagers also have a good time here).
If you have any under 10s with you then
Legoland in Windsor is also not too far from London.