Fit is paramount, as well as highly individual, which might be why people are reluctant to make recommendations. I have never shopped for shoes in London, but I would be very surprised if you could not find a shop oriented towards trekking gear, particularly near the universities. An hour's train ride to Cambridge or Oxford would certainly find you 3 or 4 such.

For socks, wool and synthetics tend to be preferred over cotton for moisture management. In the US, where most of this site's members are based, some popular brands include Icebreaker (my personal favorite), Smartwool, and Darn Tough.