Remember that your savings are measured in absolute terms. If outside London I'd earn x and spend 25% of it on housing and in London I earn 2x and spend 50% of it on housing, I'm still earning more non-housing money in London. And in the case of paying a mortgage then at the end of it all you sell the house, so the extra expenditure isn't "lost".
Quality of life comes down to personal preference. I'm not sure there's anywhere else I could live (at least without having to learn another language) and not feel any need to own or use a car, the pub theatre scene is probably the best in the world (likewise the museum collections), a huge range of musical performances, and it's the best place to find people for specialised hobbies (netrunner in my case, again literally the best place in the world for it in terms of the community size). Of course other places have their own selling points, but London has a lot going for it if you like that sort of thing.
