Zoopla's average London room rental is £552 per month. That's without adding bills, council tax, food etc. I'm well aware better value for money options exist (I have one) but you can't use that as a basis for assuming the average turfed-out social housing tenant is going to find them. Needless to say, the housing and other expenditure figures generally used in "Living Wage" calculations are much higher than that.
Of course, there's an argument that subsidising people that clearly couldn't afford to live in the area they grew up in isn't a particularly good use of funds (compared with subsidising gap years, early retirements and stay at home partners?) but I can't see the left buying it. Or anyone on the right being keen to find the extra gross £140bn pa you still need to find even once you've reduced disability and housing spend to zero.