Pay full housing costs for benefit claimants in private rented accommodation

I have recently found out that people on Universal Credit and Housing Benefit cannot get paid more than the LHA rate. This is further pushing struggling tenants into poverty. Private rented properties are normally a lot more expensive then social housing, but many tenants cannot access social housing because of the lack of it. This is putting many private tenants in the position of having to choose between being able to afford food or pay their rent.