Applying what has happened in Brixton to London as a whole is like saying Lancashire is all exactly like Nelson (which is the most tense place I've ever been to). I've never felt especially unsafe in London, I haven't been everywhere, but I've been to some quite sketchy bits on my own, on foot and it just felt more or less like Manchester or Liverpool but a bit more hemmed in.
I've been to Brixton, it wasn't the world's most salubrious place, bit edgy, but I didn't fear for my life. There's so called 'no go' (dodgy/sketchy) areas in every town. I've had abuse on streets in Wigan 'oi, dickhead, who the fuck are you' type stuff. I was mugged in Yorkshire by a guy with knife. (white guy fwiw not that it matters and I also ran off successfully without losing blood or wallet!) - Everywhere has dodgy bits. I once got collared by a gang of lads on Burscough High Street (of all places!) and told to get back on my bike and fuck off out of Burscough otherwise I'd get a kicking. This really happened. I was literally just having a bike ride and Burscough is sleepy as it gets...
There is a crime problem in London but it's just completely opportunistic and divisive to start making it race linked. Drugs, poverty and high density housing, combined with crap job prospects will create crime. Tackle stuff like that instead of embarking on a quest to say 'Race X needs sorting out'
That route is only going to lead to tears. For everyone.