I decided to look up the demographics on Wikipedia. London does indeed have a higher percentage black population than the rest of the country, but Manchester and Birmingham are very similar, whilst other major cities where you're likely to find the most tech companies have around 5%.
London: 54% white, 14% black
Manchester: 57% white, 12% black
Birmingham: 49% white, 11% black
Bristol: 81% white, 6% black
Leeds: 79% white, 6% black
Sheffield: 80% white, 5% black
Liverpool: 84% white. 4% black
Note: this excludes mixed black and white backgrounds, which make up a decent proportion of people who would describe themselves as black.
So if equal numbers of black people went into tech, and companies hired without bias, then you'd expect at least 1 in 20 people in most tech companies to be black.
You're right that fewer people from black backgrounds are applying to tech jobs, although I think it's a leap to say it's because they "don't want to". It could just as easily be that they find it intimidating, or don't believe they can do it, or they're socialised into other careers. As a company or hiring manager, if you do come across black applicants, it may well be the case that they have had to battle against a lot to get where they are, which shows grit, enthusiasm, and initiative.
