There has been considerable debate about the change in policy so that tenants in Social Housing have to pay for any spare rooms in the same way that tenants in Private Rented properties have to pay the extra rent for a spare room.
The difference in Social Housing is that the rent is subsidised and housing benefit pays all of the rent apart from the spare room. In Private Rented rents are higher and if the rent without a spare room is greater than the lowest 3 in ten properties in the area then housing benefit is limited to that amount.
In a home (flat or house) there is the basic household which could be a single person or couple with or without dependent children. However, at times there might be "non-dependents" in the household. Those are normally adult children who have grown up, but not left the house. They could include a grandparent (or two). Additionally there can be lodgers (aka Sub-tenants) or Boarders.
A non-dependent is defined as someone who lives in the household, but on a non-commercial basis. A lodger is a sub-tenant who is living in the property on a non-commerical basis and a boarder is a lodger who eats some meals provided by the tenant.
As far as Social Housing goes (Housing Associations, Council Housing, ALMOs etc) any adults be they non-dependents, lodgers or boarders are included in the calculation as to how many rooms are needed. For non-dependents there is a "non-dependent deduction". For a non-dependent on benefits this is £13.60 per week. This might be less than the spare room payment (aka Bedroom tax) or it might be more.
For a lodger the tenant is allowed to keep the first £20 per week before any benefits are reduced, but there is no spare room payment. For a boarder it is the first £20 per week and then half of any greater sum (hence if someone pays £30 a week for boarding the tenant gets £30 and benefit is reduced by £5 (meaning the tenant keeps £25 per week).
I must stress that taking in lodgers is not something everyone would want to do. I personally have often had lodgers or shared accommodation with others. However, there are circumstances where this would not be appropriate.
However, if you think of a single man occupying a 3 bedroom flat. Say the rent is £80 per week. The spare bedroom payment is £20(25%). If the man has an income of £71.70 he is left with £51.70. With two lodgers he has an income of £111.70 and does not have to pay for the spare bedrooms.
The government wishes to see the spare bedrooms being used and to reduce rents more generally which is why the government is encouraging people to take in lodgers. I am currently trying to find out for certain if LHA will pay the £20 (It will not pay the non-dependent contribution).