There's a lot to worry about if you have kids in London, drugs in schools, muggings and knife crime, general street safety, pollution.
It's definitely concerning reading the headlines. Unfortunately it's happening in other areas too - although probably not so much in the leafy shires. But then there are other problems.
London's draw (apart from family and familiarity for those born there) is the diversity, tolerance of incomers - the lack of insularity.
Not every part of London is rife with violent crime - which tends to be inter gang warfare (I wish the government would tackle it and help those affected).
Lots of perfectly safe areas especially for families. I wouldn't panic. Remember many of the people leaving won't be doing it by choice. It will be because they're priced out (made worst by Sunak further inflating the house price bubble). It's not just FTB. Growing families can't afford to upsize.
It's varied where people go. Lots just return home, to the city or town or village they come from.
If you're personally happy where you are and can afford to stay, I'd say stay. Are the schools good in your area? If people are leaving at primary age, is it the secondaries? You could try looking at other parts of London if that's the case.
School wise, some families who want grammar go to Kent or parts of Essex. Kent is full grammar.