Hi, we were in a similar position 8 years ago, moving to Claygate, which is known as the first village in Surrey.
In reality it’s only a 10 minute drive from Surbiton but feels like a more rural community because it’s surrounded by green belt, so somewhat cut off from the suburban sprawl that surrounds it.
Claygate is a lovely community, where you’ll find many like-minded families who’ve made a similar move down the A3 out of London.
We are lucky to have decent connections into London (x2 trains/hr - approx 4mins) and have a good bus service too.
Schools are good and there is an excellent secondary school in Hinchley Wood (if you can get in!!)
There are plenty of playgroups and activities for little ones, and we’re lucky to have 4 pubs, several restaurants, a thriving ‘Parade’ which includes many Surrey ‘award winning’ stores and all that, as mentioned above, open space to explore and enjoy.
The only downside is that it’s popularity means that those houses that do go on the market get snapped up very quickly.
There are however some great areas nearby that may also be worth a look. Hinchley Wood, Thames Ditton, Molesey and Cobham.
Good luck with the move. We certainly never regretted it!