I was reading a thread about living in London on a salary of ?17k - clearly it is possible but it did seem a bit tight - no money for any extras. Now the upside of London is that there is still so much you can do for free - parks (summer of course), museums, galleries etc and still frequently free (unless you go for the special exhibitions).
Whereas I think groceries are broadly similarly priced across the UK in the main chains (local stores can vary) things like eating out, accommodation, entertainment are vastly different. But as with a lot of things, if you know where to go things can be a lot cheaper.
Yes I would say you can live ok on a salary of ?17k in London but you will most probably need to share accommodation and live in zone 3-5 for that.