This is an issue that some people are quite happy to ignore. That, along with the fact that the "welfare" bill also includes pensions. Back in the dim and distant past, my rent was about £40 a week for my two-bedroom council flat; had I been privately renting, the bill to the taxpayer would have been significantly higher.
I haven't heard anything from the new government about abolishing the "bedroom tax"; a scheme that punishes people for being unfortunate enough to be allocated a house that's too big for their needs, while at the same time there are few opportunities to downsize.
Indeed, I do wonder if a better option would have been to have offered incentives to move to a smaller place, for example you get half the rent difference as extra benefits for the first 6 months, then it drop by 5% points every 6 months (45% for months 7-12, 40% for months 13-18, etc.). For each smaller house (after the second) you turn down the starting point drops 5% points (so turn down 3 and you start at 45%).
Ultimately it works have saved money, but would have made people want to downsize when they could. It would have also given them moving money, so they could do things like to put down flooring if they were moving to a council house (as upon first rental they have, basically, none), pay some removals costs and do a bit to make the house more homelike.
It costs a lot to move house (even if you move your own stuff) so the extra cost you have to pay in bedroom tax is going to mean fitter baby is a long time of paying it before you're better off by being in the correct sized home.
It's also unlikely to have actually generated much money after the admin costs, at least not for the first few years, and even then those managing it have got to keep on top of which children are still at home, what age they are and so on, so that you are taxing everyone correctly.
Of course, there's loopholes, like having a lodger or being of pensionable age (although there some complications with these) and so those managing it then have to also manage those too.