Tenant served notice but says won't move possessions!

Possession - Section 8 and Section 21

I am aware that I may be posting in the wrong section but couldn't see another more relevant section, moderators please do move to another section if this is inappropriate here.

I have a 12 month AST with a tenant whose housing benefit is paid direct to me by the council as she was in two month's of rent arrears from the beginning of the tenancy (2010). I used the 2007 RLA AST agreement which states that she must "give one month's notice to end it". I received a voicemail from her father on 17.4.13 stating that she no longer wished to live at the property due to an attempted burglary (no damage and no access gained). I was unable to contact her or her father so confirmed my acceptance of this in writing on 18.4.13. The tenant contacted me on the same day and confirmed that she didn't want to live in the property anymore. I made arrangements for prospective new tenants to view the property and during the viewings inspected the property to find it in a shocking state requiring much remedial work. Since then the tenant has told me that she has been informed by the council that she has made herself intentionally homeless by giving me a month's notice and has asked me to serve notice on her. I have explained to her that to do this would involve section 21, possession order etc etc which as everyone knows will take a long time. The tenant has told me that she is no longer staying at the property and is now staying with her mother (and has given me that address to send correspondence to )but there is no space to move all furniture and possessions and that she will be unable to move them until she has found somewhere else to live. I have written to the tenant at her mother's to confirm that I have accepted her notice and to document that despite repeated requested by phone and text message the tenant has not told me that she is retracting her notice and wishes the tenancy to continue.

My problem is that the prospective new tenants seem very reliable and have offered to help with remedial works as they are keen to move in ASAP. I would therefore like the current tenant to move out. I have sought advice from a legal advice help line who suggested that the AST does not require her notice to be in writing and as such it still stands. They explained that if she leaves possessions in the property at the end of the notice period then I will need to apply for a possession order followed by bailiffs to lawfully evict her. I also understand that I would need both if she has not given me keys back.

Any advice on the accuracy of the above would be appreciated!