I live in Reading and I often take the train into London, I have never in my four years of commuting ever had a seat regardless of the time I chose to embark, these trains are every half an hour in peek time and comprise very large trains.
I mention this to make a point people travel to London from Reading, people who are permanently employed in London and some who wage permitting would choose to live in London. They are forced instead of dwelling in London to wake up pay to stand on a crowded train and then on a packed underground train just to get to work.
Meanwhile some fictional family is living in 400+ a week accommodation not having to face the daily trek to work or suffer any crowded transportation and who pays for whom? It is the hard working, down at heal commuter that pays for the extreme rents charged, the very same rents that force the commute to undergo the drudgery of the daily commute, and this is supposedly fair and right?
Add into this a very important consideration, since when was it the job/duty of the state to ensure economic multiplicity in boroughs in the capital? Since when did economics multiplicity matter? Indeed until the birth of the modern state any concept of economic multiplicity would have been alien and people would have been forced at best to move if they lost their jobs.
In the end a cap on housing benefit is the only way to control the rent we pay to private landlords and thus accidentally subsidise the buy to let boom that has prevented so many hard working families form funding a permanent house and also to reduces the burden of housing people in expensive areas.
Yes people will have to move and yes moving is unpleasant and commuting is unpleasant but people who work have to do both of these things in order for the circumstances to meet there income and while I would never support a policy that made people homeless and I mean actually homeless but I do support a policy which makes housing more realistic