You appear to have answered your own question! If it's a
private rental (rather than one from a local authority or housing association) then the so-called bedroom tax is irrelevant.
Equally, the actual rent paid is irrelevant. The Local Housing Allowance he would be eligible for would simply be based upon the rate for a ONE bedroom property, irrespective of the actual number of bedrooms in the house which he was renting. You can find out how much Housing Benefit (LHA) he'd receive (subject the the usual eligibility criteria) here:
https://lha-direct.voa.gov.uk/search.aspx
Any excess he'd then have to fund himself.