Apparently, the majority of recipients of housing benefit* are actually already in work. This leads me to a very short rant:
If rents are such that people can be working full-time and still require housing benefit, this means that either wages are too low, or rents are too high, or (most likely) both.
(That was the very short rant. And now, here's a slightly longer one...)
Honestly, a benefits cap per family is a good thing. And placing the cap at the average household earnings is, if anything, overly generous. But it doesn't work in isolation if (as is the case) people who need to live in London for their jobs cannot afford to live in London without those benefits.
(In fact, I'm inclined to think that there should be no such thing as housing benefit. Instead, those who aren't working, for whatever reason, should be given a much higher general benefit (and expected to live on that), while wages and rents/mortgages should be placed so that those in work don't need benefits to top up. As things stand, the government is essentially subsidising lots of landlords who are charging too-high rents.)
* Or whatever it's actually called.