Yes, in some cases you may be able to ask the court to order that the property is sold, even if you were not married. This would not be dealt with under divorce or matrimonial finance law. It would usually be dealt with under the Trusts of Land and Appointment of Trustees Act 1996. You would normally need to show that you are either a legal owner or that you have a financial share in the property.
If the property is jointly owned and one person refuses to sell, the court can decide whether the property should be sold and how the money left after any mortgage, costs and expenses should be divided. If the property is only in one person’s name, you would first need to show that you have a financial share before asking the court to order a sale or decide what share you should receive.
The court has more limited powers than it would have on divorce. It will not divide property simply because that would seem fair. Instead, it will apply property and trust law. The court will look at things such as ownership documents, what each person intended, financial contributions, and any agreement or understanding between you. If children live at the property, their housing needs may affect when a sale should happen, but this does not automatically stop a sale or create a property share.