This is almost as emotive a topic as the whole school saga?!
We are definite Londoners for life...what child is ever going to turn around in 10-20 years time and hold against you an amazing upbringing in London, as opposed to being stuck in some small town with limited opportunities forever?! When we had our first son, who is now 13, my Aunt gave us some good advice : never move your life just for your children as they will grow up and move away as soon as they are old enough. Far better you are a happy parent in the environment which makes you happiest so your children can have the best side of you.
Big gardens and houses are overrated... As soon as the kids are at school, no garden is big enough for their ball games and having a big common close by to walk to is a far easier option. We all have to choose what is best for us and naturally that is something which is different for each one of us...for us that is the community we live in in London and all the fabulous things on our doorstep including a slice of real urbanity to expose our kids to from an early age. Good luck in your decision- in my experience the grass will always appear greener elsewhere?!