I've lived in London (even fairly recently) on 32K :-) No kids, but a non-working wife... I have a bad habit of taking jobs that look like fun rather than pay well :-D I'm not being sarcastic when I say that you can probably draw that line pretty arbitrarily and make a pretty good case that you are giving up something crucial if you go below that level. Even being single, though, I think it would challenge the most frugal person to live on less than 25K in London. For a spouse and 2 kids... a heck of a lot more, to be completely fair.
We were quite comfortable on 32K, but it was tight and we couldn't save any money. About 12K for a nice 2 bedroom garden home (in lovely Watford ;-) ), 6K for taxes, 5K for the train, 2K for food, 2K for utilities, clothes, odds and ends and a quick holiday in sunny Bath :-) rounded it out (the tax number may be wrong -- I don't really remember).
Despite the horrible commute, living outside of London and commuting in improves your standard of living pretty dramatically IMHO. If we ever go back, I'm thinking of living even a few stops further out: you pay exactly the same amount of money on housing and transportation (the housing market is efficient), but you get a much nicer house -- at the cost of time...
Although, I say that... This year we stayed in a friends house in Millwall for a month and my commute was worse than from Watford (although a heck of a lot cheaper). So even being in Zone 2 doesn't guarantee you a good commute.
