Council help for tenant at end of section 21notice period

Possession - Section 8 and Section 21

A superb tenant who has been with us for 9.5 completely trouble free years has been refused full housing benefit having been told she would qualify as a mature student with children. She has been through the appeals process and it would appear was wrongly advised by the HB people in the first place. She cannot afford to stay with us (£600 per month short so no room for negotiation). We have served a Section 21 notice for beyond the fixed period of an AST giving 2 months notice from a rent date all as per the RLA download and she has signed receipt of a copy. She should leave by mid August. She is being advised however by her local London Borough that she should not move out but force us to get a court order before they will consider her and her children for rehousing. Is there anything we can do to help her get rehoused and to avoid her and us all the hassle of involving the courts?