If you have gained an interest in the property this is called a beneficial interest. This beneficial interest can not only entitle you to a share of the money if the house is sold but can also mean that you have rights to live there that you wouldn’t have otherwise had. It can also enable you to prevent your partner from selling the home or using it to get a loan of some kind. In the absence of any kind of written agreement the court will look at whether there was an implied or constructive trust that you should have an interest in the property.
However, even if you gain a beneficial interest, it will not necessarily be of an equal value to that of your partner.
If your partner is asking you to leave their home and you believe you may have a beneficial interest it may be possible to go to court and get a injunction which would enable you to stay in the house until the full court hearing about your case.
This is an extremely complicated area of law and before doing anything it is very important to get expert, independent legal advice.