Surrey is, outside of Central London the most expensive place in the country. This is because it is the absolute monkeys pyjamas.
It's near that London
It's absolutely beautiful
It's full of nice things
It's easy to get to other places from.
I'd recommend East Molesey, just urban enough but 20 mins from the country and right by the Thames. Still quite cheap too.
My grandma lives there and my dad grew up there. I lived nr Guildford until I was 14.
Yes it has some countryside but it's so damn crowded that you can't move, it has no "real" identity (it's not rural and it's not London) andm it's the worse place in the UK for "the Joneses" of this World.
Moved to Cornwall aged 14 and it was the best thing my folks ever did.
To the OP - South could be an option - Winchester is pretty nice and the outskirts of Bath and Bristol are good too.
If you don't need access to London, the SW is amazing. If you want "proper" MTBing country, look nr Dartmoor or Bristol (for access to South Wales).
Have lived in Surrey, Swansea, Bristol and Cornwall. Cornwall wins hands down BUT only if you can find decent work. Otherwise it's a PITA.