Just show them this video.
If you don’t have any racist friends, just read the comments (don’t read the comments, ever).
When I’ve visited London (or New York, or any cosmopolitan city), I’ve always enjoyed the diversity — it’s a good thing. I’m also happy when everyone can feel like their wonderfully complicated place is home. There are plenty of white people in London who also feel it is their home — why should they also have this sense of exclusivity? We can all be home. If someone else feels at home in your city, that doesn’t mean you can’t also feel at home.
If you think “home” has to be a place where the only residents have the same complexion that you do, that means you’re a racist. It’s a pretty easy test.