I think it would be use and occupation charges rather mesne profits, although the same thing in practice (the former applies to people who never were a tenant, the latter to former tenants after their tenancy has ended). In both cases, these are normally awarded by a court as compensation to the landlord for loss of rent during the period when the unwanted occupant was living in the property and defending proceedings to get them out.
Occasionally landlords will ask for these payments up front in advance of getting an order from the court, although most landlords are extremely cautious about this in case they inadvertently create a new tenancy agreement by accepting rent.
What does this claimant intend to do with her HB payments if you make them? If she is not being asked to pay money to the HA, I cannot really see what point there is.
I would be thinking along the lines of refusing the claim on the basis that there is no liability to make payments unless and until the court says different in the proceedings that the HA is presumably pursuing to get her out of the property.