'Right to remain' after tenancy agreement ends

Other

Our tenant is due to move out on 3rd August but has been told that the house she is to move into will not be ready until 15th August. The rent is funded by West Oxford DC Housing Benefit. She has requested emergency accommodation and they have told her that she has 'the right to remain' in the property and will not give her emergency accommodation.

The reality is that we house will remain empty until 20th August so we could let her stay but ideally in a legal and legitimate way. My questions are then:-

1. What is this right to remain law?
2. If she stays the additional days - how can we get this under some legal agreement that covers us as landlords?
3. We are planning to move back in ourselves on 20th August - what options do we have if she is still in the house on 20th?

Thanks

Mike