Do not underestimate the cost and hassle of a long commute, even if only 2 or 3 days a week. People will always lie about their commuting time, they will say half an hour when in reality it's at least an hour door to door on a good day, and 90 minutes on a bad day.
Also bear in mind that, after they reach 11, many kids couldn't care less about a big garden, and would much prefer the amenities and ease of getting around of a city - so be prepared to act as a chaffeur for the kids.
There was a good discussion here:
https://www.mumsnet.com/Talk/property/4 ... -SW-London
I say all of this because, even if you are absolutely determined to leave London, these remain important points in deciding between "out" and "out out".
Also, and I know lots of people will hate me for this, if you are not English white (not even British, but specifically English) think twice about going "out out": integrating with the locals may be very tough, all the more so for kids at school.