No-one's mentioned the impact of high rents on the benefits budget.
I'm retired now, but worked (wholly or partly) in welfare rights for 25 years. I've gone through the nitty gritty of thousands, if not tens of thousands, benefit claims and calculations in that time, and the housing benefit/housing costs element of UC, has been the biggest single item in most of them. I'm in the SE region, where rents are the highest outside of London.
A lot of people in work and claiming UC wouldn't be eligible for UC at all if they weren't paying high rents, and it's rare for the full rent to be included in the UC calculation. The average rent here is £1750 pcm for a 3-bed, but UC will only include £1450. A huge chunk of UC, often all of it, will be going to their private landlord. (On a recent calculation I did for a single parent with 3 kids, considering taking a job at a salary of £37k, the UC entitlement was around £1400, and their rent was £1800.).
Someone in social housing with 3 kids would be paying around £750 a month for a 3-bed, so their UC entitlement would be much lower than someone in private rented accommodation.
Building more social housing would reduce the "benefits bill".