How much is somewhere in say Stevenage? When I used to go to London a lot I could consistently book into Premier Inn/Ibis in Stevenage for a max £50/night (often even cheaper than that!) which was much more attractive than Central London hotel prices and just 20 minutes or so to/from Kings Cross with services running until around 2am to get back
Granted you would have to take a season ticket into account, £4k / £5.4K Z1-6
My friend got a job in Surbiton many years ago, they shared a flat with a friend and it was something ridiculous like £1400 / month, stayed over a few times and you certainly don't get a lot for your money! The friend sacked it off after a few months and then my friend didn't last much longer as it was impossible to maintain payments on that alone (plus I think they quickly grew bored of 'London life')
I live in Yorkshire and over the years working in IT have grown my salary to £39K, which will grow to £44.5K...doesn't include any management responsbility either (1 in 7 on call is part of it, but compensated for), I've looked at comparable London based roles in the past and they certainly wouldn't even touch the sides of the increased living costs