If you have drawn up a cohabitation agreement with your ex-partner then your rights on here may be enforceable through the courts if you break-up.
If your ex-partner owns the property, unless you have somehow acquired a beneficial interest, then you will probably not be able to have any kind of claim on the property. There are some situations where you may have acquired a beneficial interest in the property. You could have paid towards the mortgage or deposit or maybe even done some home improvements which have increased the value of the property. However, this is a very complex area of law and you would need to get independent legal advice before pursuing any claim for a beneficial interest on a property.
If you own the property jointly with your partner (your name is on the purchase documents or any deeds) then you are entitled to your share of the property, as stated on these documents.
If you are unsure where you stand with regards to your finances and assets after the breakdown of a relationship then it is very important to get expert legal advice as soon as possible.