Private schools with commutable distance to London

[Everymorning]

Hi -
I am a new mum to a new born boy. We are looking to relocate into an area that has great private schools and is also commutable to London. I am not from the UK originally so would love some advice/thoughts if possible please:
We've been doing some research and it seems like there are only limited options -

• Kent (Sevenoaks) seems to be an obvious choice
• Surrey - Esher seems to be possible but not too sure where else?
• Hertfordshire - for haberdashers but again we might be missing other schools there? St Albans?

Also looked into Oxford (Dragon School, Summer Fields) and Cambridge (The Perse) although the train service means commuting to London on a daily basis could be a big challenge so we are almost ruling them out.

I'd be very interested to hear views on what schools/areas we have missed.

A second question is in relation to types of schools - from the list you can see I am considering different types of schools - namely

1. Sevenoaks (seems to be more "modern", academic)
2. Dragon schools (seems to be more traditional and leads to more boarding school route) and
3. Haberdashers/Perse (where a child can stay through from age 4-18)

Frankly speaking I haven't found a great deal of information in terms of how to choose the types of schools, and to even understand there are three types took quite a while already!! It would be so helpful to hear thoughts on this generally too.

Thanks so much!

Have a look at Eaton Square Nursery Schools. I heard it's a great school and I think it's also accessible for commuters.