Lots of people don't cook wherever they live.
I couldn't put my finger on what was odd about a boyfriend's London flat until it dawned on me that his tiny kitchen - it was a large windowless cupboard, really - didn't have a cooker. Just a microwave, a small fridge with milk and alcohol in it and a small sink. One cupboard with bread and cereal in it.
He had four plates, four bowls, two mugs on a mug tree and some cutlery hanging from one of those dangly things from Ikea. Lots of wine glasses.
It took about two months for the penny to drop because we used to go out all the time and eat cornflakes or bacon sandwiches the next morning.
I live in London. I have a decent-sized kitchen with a window and full complement of white goods and I'm going to cook tonight. But I don't eat in every night.
Like PPs have said, part of the attraction of living in London (or Manchester or Leeds or Birmingham etc) is that you can eat out. Within a minute of my house there are eight restaurants. Within five I lose count.
I like Brixton, OP. I like the centre, and I also like the hill, but I'd prefer to live closer to the station. But I prefer where I live.