Then the Bluebell Railway is for you and little tigs, tigger: It is a superb operation (I would say that because Mrs NJ and I are Life Members). It is one of the country's premier heritage railways. You can get to it by train - its station at East Grinstead is next to the National Rail station. If little tigs is mad about trains I'm sure he'll love it:
https://www.bluebell-railway.com/
If you want to head west there is the Watercress Line:
https://watercressline.co.uk/
It runs from Alton to Alresford in Hampshire. Again, you can get there by train, about 40 mins from Woking. The Watercress line shares Alton Station with National Rail.
If you fancy a miniature railway, the Great Cockrow railway near Chertsey is excellent:
http://www.cockcrow.co.uk/index.html
You really need a car to get there but it's a really good day out. It is a one-eighth scale (7.25 inch gauge) railway where you can get really close to the trains.
Happy Chuffing!