As
@Dave implied, it depends on what part of the country, or possibly even what part of London, you live in.
If you live in South London or the Surrey/West Sussex-type area, I imagine it is quite easy.
For me in Gloucestershire, however? According to TrainLine, Lydney to Chessington South would take me a minimum of
4 hours and result in a minimum of
3 changes (Lydney-Newport, Newport-London Paddington, London Paddington-London Waterloo, London Waterloo-Chessington South). Even if I went from Bristol Parkway rather than Lydney, it would take me a minimum of
3 hours and result in a minimum of
2 changes (Bristol Parkway-London Paddington, London Paddington-London Waterloo, London Waterloo-Chessington South). A return train would also cost me a minimum of
£103 from Bristol Parkway or
£115 from Lydney.
By comparison, the drive time from my location to Chessington is currently showing as
2h 9m (albeit I think this is probably at the faster end of the scale; I imagine traffic is relatively light at 11pm).
Once you're at London Waterloo, it seems pretty easy to get to Chessington via public transport. The problem is that you've got to get to London Waterloo in the first place, which for much of the UK population is easier said than done.