Where to buy a house?

We are 30 y.o. and our daughter is 2y.o. We have almost 200k￡ of savings and our family saves approximately 50k per year. Both of us commute to the offices in the center of London 1-2 times per week. We are renting a flat in the West Hampstead area, and we love it. But we want to buy our own property. Main wishes are (ranged)

• 3 bedrooms
• great primary and secondary school
• the safe and family-friendly area
• garden (for barbecue, kid, dog, and gardening)
• park, cafes, and pubs within walking distance.
• good services are a plus.

I love West Hampstead/Hampstead, but the price range here for 3br house with a garden starts from 1.6M :( As I calculated we can spend on our property ~800k.

Honestly, we don't use London lifestyle things like theatres, exhibitions, festivals, etc. Even in cinema we go 2-4 times per year. But we like parks, cafes and traveling. I also appreciate good services (delivery service, private medicine from insurance, coffee/wine subscriptions, etc.). So probably it would be reasonable to find a place outside London. We are looking at St. Albans, Hitchin, Reading(Caversham), and other towns.

What do you think about it, what would you do in this situation? Many thanks in advance for your pieces of advice, thoughts, and just opinion.

,