here is your necessary know how
Chislehurst YES lovely, great little village but actually, £650 wont buy much!
Trains brill, 20 odd mins to Victoria or London Bridge
Petts Wood
Amazing little place but pricey. Little parade of shops by station. very sought after. Mostly 1930 stock of houses but HUGE ones. trains to Charing X Cannon St and London bridge, also perhaps Victoria
Beckenham at a push is nice and again v pricey.
Sidcup much cheaper, high street not up to much but Waitrose is coming!
£650 would get you a detached 4 or 5 bed Victorian and there are plenty around
trains 30 mins to Charing X Cannon St or London bridge
Blackheath how could you forget Blackheath. Not sure on prices. But ticks all other boxes. 20 mins into london.
Schools - well if you are in London boro of Bromley, there are good schools depending where you live, the secondarys are good. They have a grammar system for top 5 % or so, one boy and one girls school. Got to be mega brainy
London boro of Bexley has 4 grammars, top 20%. One boys one girls and 2 mixed.
Also can sit Dartford grammar exam and got to pass it to get in. about top 20%
To be honest, those who dont get grammar can still get VERY good education in Bromley and Bexley but you need to live on top of good schools to get in. Some examples
HUrstmere boys and Blackfen girls SIdcup
Coopers Chislehurst
Hope that helps a bit