If you have been paying into the mortgage or have helped with the deposit you may have gained some sort of interest in the property. If you are in this situation it is essential that you get expert legal advice, especially if the relationship is breaking down and you think that your partner might assert his right to ask you to leave.
In order to try to prove that you have some sort of interest in the property then you would need to go to court. During the proceedings you should show the court that you both agreed that you should have an interest in the property or, alternatively, the court could look at both of your actions and see if an agreement was meant to be made that you should have an interest.
There is no specific area of law designed for cohabiting couples. This means that this area of law can be highly complex. We strongly advise that you seek legal advice before starting to separate financially as starting to separate financially without the correct legal advice can complicate matters further.