The Housing Costs Element for a claimant renting a private tenancy is based on their Local Housing Allowance.
However if their actual rent is below their Local Housing Allowance the DWP will use this lower rate.
This means the amount of Housing Costs Element included in the Universal Credit calculation for a private tenant will depend on the size of property they are deemed to need, regardless of the size of property they are actually living in, and the range of rents for a rented property of that size in the area they are living in.
Some claimants are deemed to need only a room in a shared house (the Shared Accommodation Rate); and regardless of family size no-one is regarded as needing a home with more than four bedrooms
Private landlords can apply for APA managed payments to landlord using an online Direct Rent Payment service:
The government has produced a short illustrated guide for private landlords: Helping Your Tenants: link on this gov.uk page (Touchbase magazine).
LHA rates available from a government website here.