A popular question from campers, there's a few ways to do it. Here's what we recommend.
Train from Ashtead
Ashtead Station is approximately 25 minutes walk across Ashtead Common from here. It's a nice, peaceful walk and pops out right by the Station. The route is out past the cafe, up the hill towards the metal gate. From here, go straight on and don't turn off this path until it pops out on the other side of the Common.
There are 5-6 trains an hour from Ashtead to both Waterloo and Victoria, and an adult off peak day return ticket is £12.60. NB Ashtead is not on the London Oyster Zone Map.
2. Bus to Surbiton, then train to Waterloo.
The 465 bus goes to Surbiton from opposite the Shy Horse pub at the end of our road twice per hour (check timetable here) and also check CityMapper on the day as the buses often run a little bit late.
It's around 20 minutes to Surbiton, from where there are loads of trains to Waterloo each hour, with fast trains taking around 20 minutes.
This journey is all in the Oyster Zones and can be made entirely either with an Oyster card or contactless debit card with no need to buy a physical ticket.
If you return the same way in reverse, you can also get a taxi from Surbiton back to The Barn KT9 if the bus timetable isn't helpful at the time.
Those are the two easiest ways in. You can also walk to Chessington South along the A243 and get the train from there, or to Epsom across Epsom Common which are both around 40-45 minutes walk.
If you're cycling, the direct way is around 30km to Central London, this is the route I used to commute in every day which works pretty well.