This is so complicated and PC rules these days are so complex. I lived in London for about 5 years in the early 00's - I was young when I moved there and whilst I'd moved from one city - Glasgow to a bigger one - London, I was initially quite fearful of going out and about. This was more to do with not knowing the landscape than any kind of racial fear.
I lived in Peckham initially then moved to rent a place in East Dulwich - before I continue I'm not sure when this piece is set because Peckham these days is very gentrified (run a Right Move search for property values and you'll see what I mean.) It's moved on since the Del Boy days. Homeless people are everywhere in London - and most seem to have Glaswegian accents for some reason!!
The character here - I'm not sure is she fearful due to being unsure of the landscape due to it being alien to her? or is her fear born from news items describing 'another stabbing in London' or purely because she's not used to black people?
it is a valid point - Glasgow has a large Asian (India/Pakistan/Sri Lanka) population but not many black people, when I moved to London it surprised me, but the first two people who befriended me at the new job I'd moved there to take, were two black guys (I'll call them Ken & Hassy coz that was their names LOL) and I pretty much hung about with then for the whole 5 years I lived there. I still see Ken when I go down there, though Hassy moved to Germany in 2010 and we lost touch.
The group I ended up being part of were very mixed - black girls with white boyfriends and visa versa and whilst there were racist comments occasionally on both sides most of it was in jest and based around stereotypes and stuff and alcohol!
There were a few ill mannered morons we came across that would do the monkey thing and a few resented white girls being with black guys - Ken was psychiatric nurse and his white girlfriend Karen, (wife now) was a doctor - I found that the integration of the black kids and the white kids in Peckham was fine and most folk didn't even think about it. Initially, I'll admit to being a little uncomfortable walking about at night with Ken and Hassy in case anyone decided to have a go, but it never happened.
When I watch the news now about black gangs and territorial ghettos - that isn't the London I recognize or lived in. Things might have changed but there are people with agendas out there that tend to overplay these things.
Not sure this helps that much but hopefully the insights might help...