Hello,
You may well have moved by now, but having made the same leap from London to a village near Thame I thought I'd share the experience for others doing the same.
We have found the string of villages from Long Crendon -> Chearsley -> Cuddington -> Dinton to all be great places to live. Each has a decent pub and community, is within a mile or two of Haddenham & Thame parkway station (with super reliable and fast services into london), and have Cuddington & Dinton primary school (which is great school by the way) on the doorstep, and Long Crendon Primary which is also very well spoken of.
Long Crendon & Chearsley are both close enough to Lord Williams in Thame for for secondary school catchment - this year lord bills had admissions from stone which is even further away than all of these villages so it is very year dependent. Otherwise Waddesdon has a very good CofE secondary if grammars/11+/tutoring from year 5 etc aren't you or your childs thing (but that will involve attending church in the lead up!)
The villages themselves are an interesting mix of very pretty old thatch cottages, village greens and churches, pubs and a shop in all of the above aside from Dinton (which has a strange Belgian restaurant instead) and more modern housing developments which are less appealing to the eye but provide cheaper housing stock!
There are good communities in all of the villages, they all have play areas/pitches and clubs/activities to keep the kids occupied after school.
Thame is slowly but surely, almost grudgingly, becoming more like marlow for example with cafes and shops, but at the moment still has rural charm and the rural roots are still quite strong especially market day. Make no mistake, this is an area with a strong agricultural roots and by moving here you are leaving behind services on tap, ease of transport and the selection of places to eat and drink you will be used to in London.
BUT - traffic is minimal, air is clean, nobody is getting stabbed, people are friendly and welcoming, getting to anywhere in the country (including heathrow) is straight forward and the countryside is really beautiful - there are so many amazing walks right from your door. This is the thing we've enjoyed the most.
If you're hankering for a slice of London style/glamour, you can go to soho farmhouse which is 45 mins away.
In comparison to other (perhaps slightly more sought after) areas nearby (Berkhampstead, Great Missenden, Great Milton, Henley) the area represents far better value. Prices are possibly dragged down by Aylesbury (6 or so miles away) which lets face it is a bit of a blot on the landscape, but which has a selection of retail shops/outlets/activities that are sometimes very useful. On balance, I'd rather it was there than it wasn't!
Hope that helps weighing things up!