It's true. Almost a majority of originally East End white families moved to Essex and Kent. I've also read reports on Essex and Kent nowadays being filled to the brim with drug traffickers and crime bosses. The East End in general doesn't have the gritty, homegrown working class atmosphere anymore. Some areas have undergone major redevelopment and most are populated by descendents of the Jamaicans and more recent Bangladeshi and Pakistani immigrants. Even Canning Town -a traditionally very white area- nowadays has around 30% blacks living there, which still makes it the most 'indigenous' area in all of the East End
South London will probably have it's fair share of homegrown crime indeed. Most of it minor idiots with also a couple of more major British criminals operating there.
As for the Southeast Asian gangs: I've heard about Pakistani ( ''Mirpuri'' actually ) groups being involved in major drug and weapon trafficking operations as well as prostitution and smaller incidences of extortion. Bangladeshi gangs on the other hand always struck the impression on me for being little more than retail drug salers or just plain annoying pricks.

Btw, I'm not from England but the dad of a friend of me grew up in Bermondsey ( which is more South London ) and still has some contacts in those places. That's why I know some stuff on England's southeast ( and probably also why I'm very interested in British organized crime lol).