In England & Wales if you were unmarried you will need to rely on property law, the Trusts of Land and Appointment of Trustees Act 1996, and if both names are currently on the deeds it will be assumed that you hold equal shares unless it is stated differently. You can apply to court to have the property sold and the equity shared or it can be transferred to your ex partner if he wishes to buy you out.
However, it is a complicated and expensive area of law so it would be good if you can enter into negotiations and come to an agreement between yourselves. Alternatively you could use a mediator who will work with both parties to find a way forward that works for everyone, or there is old fashioned negotiation through solicitors.