Your wife has a financial interest in the property by virtue of the fact that you were married even though the property may be in your sole name.
However as long as it remains in negative equity, and a sale would not produce enough money to pay off the mortgage, then unless you or she are willing to pay the shortfall or the lender is willing to forego the shortfall, then sale is not an option. The mortgage must be cleared on completion of the sale. There would also be any agents costs and solicitors costs to be paid.
If the property was not in negative equity, then depending on whether there were children or not, she could force a sale to get her share of the equity which you acquired by virtue of the marriage, from the property. If there are children (which you don’t mention) the situation can vary considerably.
Can I clarify anything for you?
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If the child lives with you in the property, then even if there is equity in the house, unless it would be enough to buy a home for you and the child and give your wife some money, then she would not be able to force a sale.
On the other hand, if she is the main carer of the child, she could probably force you out and get the court to allow her to live in the property.
It depends where the child lives the majority of the time.