If you're willing to compromise - live in a room in a shared house, almost like a student, or somewhere dodgy (e.g. tower block with lifts that smell like piss) or with poor transport links, you'll be able to reduce that by 50% or more.
Between myself and my GF, we make about 90K GBP, and we're fairly comfortable. But we live in Bow in the East End, don't have kids, and barely feel middle class.
Most single young (under say 35) professionals in London share flats, and I'm including lawyers, investment bankers, doctors, etc.
One reason is that price drops disproportionately with the number of rooms, for example for a 1-bed flat you might pay £200/week but for a similar 2-bed you'd pay only £240/week. You could pay 1000/month for a "half-decent" 1-bed flat, or alternatively you could share a great 2-bed flat for the same price. And many people chose to make the second decision. Also it makes much more sense in terms of buying household products and makes "luxuries" such as hiring a cleaner much more affordable.
If you really want to live on your own it makes more sense to live in one of london commuter belt suburbs where you can get a flat for 600/month.
But if you have a significant other, then I agree, sharing is a whole heap better.
We live in a 3-bedroom, two-story house with a back garden that runs down to the canal, and a view directly onto Victoria Park past the canal. It's about 25 minutes from almost anywhere in central London by scooter (to my mind, the best way to get around London). The house runs to only slightly more than 1000/month.
A funny thing is that yesterday I was thinking of emailing (or should I say spamming) you to ask for advice. I have your address from some conversation we had long time ago over bpd.non-tech, and I don't know anybody in UK.
Obviously there are many people living off much less, but don't expect the same standard of living you could buy elsewhere with that money...