There are quite a few ID studios within or on the outskirts of London, but like Bengt said, there’s a crazy disconnect between salary and cost of living. Also massive competition for a small pool of ID / product design jobs. When I worked in London for a year I was heamoraging money, but that might have been because the nightlife is awesome.
I’m a UK designer and have moved around the country a lot - and the provincial cities like Birmingham/Bristol/Manchester are where to find the best pay to cost of living balance.