I owned a house back in 2001 before i came to London worth 60k, i had a job that paid 18k a year.
In 2002 i transferred to London with the same job and earned, in the same job 19.5k, i'd sold my house and made a 12k profit on when i'd bought it in 1999. I couldn't get a mortgage down here even with a 12k deposit because the cheapest i could find was way too expensive given my earnings. I rented a poxy room with a bed a wardrobe and sink in, with a shower in the corner (all one room) and a communal kitchen and toilet. I had to leave and find a better job before my savings pool ran out.
In summary even though i had more money going in my bank account every month i was so much worse off until i found a decent job. You can't compare London with anywhere else unless you have lived here or at least tried to. You need an extra allowance of at least 4k to see any benefit of the same job.