That's very admirable I must say, most unlike the usual form of questions on here.
If the house is in your sole name and she has only been occupying it informally with no strict rental obligations/tenancy agreement set up then she is occupying under a licence to occupy.
If she is still in the property then it will be difficult to sell because you will have to disclose her occupation to the purchaser on the property information forms. They will also that she signs the sale contract. If she does not then they will probably not exchange contracts in the sale.
You can evict her by giving her written notice of evictions, referring to her, you, the property, that she has been occupying under an informal licence and that you are giving her reasonable notice to vacate - this should be about two months from the date of the notice. State that there Send it by registered post.
If she does not vacate after the notice period has expired then you would have to apply for an order for possession from Court. Once granted, you could then apply to Court for a warrant for execution so that the court bailiffs effect evictions. You would then be free to sell the house with vacant possession.
In order for her to claim an interest in the property she would have to make an application to court on the basis that she has made mortgage repayments over and above rent, contributed to the financing of the purchase of it, or spent considerable money on improving the property. This would be quite an expensive application for her to make.
You should consider getting a solicitor to write a letter to her outlining the position and her options, making her aware than in theory she is not entitled to any equity in the property. If you suspect that she may sign a sale contract then not actually move out on completion then I would go with the route of eviction. Not being able to complete would be expensive for you.
My answer assumes no children.
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