I lived in Kent and London and I was making friends with native speakers at a steady pace of roughly one friend per year (and I mean friends I'm willing to keep for life). What I find quite interesting is where these native speakers came from. I befriended exactly zero people originally from Kent, one Irish person, two Londoners, two Australians and about five people from Up North. I never lived Up North.
I don't think any of these people approached me or started talking to me out of the blue. OK, maybe the Aussies did. With the rest, we just worked together and got to know each other gradually until something clicked. A good indicator for me was when they didn't care much for small talk and were happy to have a more meaningful conversation. I'm really glad this was the case because had my social life depended on my ability to engage in small talk, I would have remained friendless. Perhaps I should have attended a friend-making course :)
Another thing I noticed was that if I got on with someone I usually got on with their family as well. In my country the chances are fifty fifty, I'd say. So if you find someone you like in the UK, if you have a similar sense of humour and general mindset, go meet the family.