One of the reasons for better schools is ...
... that you get loads of cash thrown at you.
the City of London getting the most at £8,595 ahead of Tower Hamlets (£7,014) and Hackney (£6,680.05) ... At the other end of the scale, Cambridgeshire is the worst funded per-pupil at £3,950, followed by South Gloucestershire (£3,969) and Leicestershire (£3,995)
^
This. We live in Cambridgeshire, and our local primary schools are (1) over subscribed (the new one they haven't even finished building yet is already full) (2) not exactly stellar (if I'm being generous). At secondary, the position is horrific (only 36% of students got 5A* to C at GCSE inc Maths and English this year - last year was a whopping 38%!).
OP - your child(ren) will be fine, so long as you do your homework on which of the local schools would be best for them, and manage to get them into a decent and supportive school. If, on the other hand, your local school's OFSTED reports, results and the atmosphere you experience when visiting the school make you worried, then you may want to consider other options (including moving).