Alternatively, the Court could conclude that there was no initial agreement between you and the legal owner to share a beneficial interest in the property but that this altered over time.
This is referred to as an ambulatory trust. An example of this is when one party may finance an extension or major improvement to the property so that the home is completely different from when it was originally purchased.
If there is a dispute with your partner about the property, you could seek to negotiate a settlement and agree on whether you have an interest in the property, whether the property is to be sold and how any equity in the property is divided.
If you are unable to reach an agreement, you do have the ability to issue court proceedings.
The Trust of Land and Appointment of Trustees Act 1996 (ToLATA) gives the Court certain powers to resolve disputes about ownership of land.
A cohabitee whose name is not on the legal title of the property can make a court application under ToLATA for a declaration that they have an interest in the property, an order that the property be sold and an order as to how the net proceeds of the sale are to be divided.