Are you unmarried? When a couple cohabit contract law or complicated trust law in relation to property [Trusts of Land and Appointment of Trustees Act 1996] has to be relied upon. Where property is held in joint names, the law assumes that it is held equally, ie, 50:50, unless there is evidence of an agreement either verbally or in writing that the shares are in some different proportion. Your ex partner would be entitled to a her share of the equity and could make a court application to force a sale.
If the deeds are in your sole name she could establish a resulting trust (when one party has made a direct financial contribution to the purchase of the property in the other's name) or a constructive trust.
A constructive trust is where there is an express agreement, arrangement or understanding between the parties or when there is no express agreement etc the court may in some cases regard the matter as if there had been one. If someone not named in the deeds of the property contributed directly to mortgage payments, or paid for substantial improvements the court may infer that this must have been because there was a common intention to share the property. People do not usually pay other people�s mortgages for nothing. Less important contributions, like contributing to household expenses, are no indication there was common intention to share the property.
If you are married it is a completely different ball game.