The North Downs is one of the most easy to access by train riding areas in the country.
If you’re coming from London, Dorking or Box Hill are the best stations, good trains, and you can ride off road from about 1/2 a mile from the station if you want, or do a 3 mileish road blast to the most popular trails. Holmwood is very good, but doesn’t have many trains. Gomshall is also bang in the middle of the trails, but again, you usually have to change trains to get there, meaning it’s quicker to ride from Dorking or Box Hill.
I believe you can ride out from Guildford too if you’re coming from Hampshire or somewhere, although I don’t really know that end.
Joe