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My name is ***** ***** I shall do my best to help you
In fact the solicitors are wrong.
Yours was not an "assured short hold tenancy" since you shared a property with the tenant
Accordingly you did NOT have to protect the deposit and you can deduct the amount she owes you from it
I hope that this is of assistance - please ask if you need further details
Whatever it said on the agreement it does not fulfil the requirements necessary to be a Short hold tenancy so it was just an oddly worded lodger agreement!
I am sorry that you feel that my service was poor
Your contract is void as an Assured Short hold but stands as a lodger agreement and yes you can take the months outstanding rent from her depaosit