When partners decide to live together the easiest option is often to move into the property owned by one of them.  As part of sharing the outgoings, you may agree to share the mortgage payments as this is a major financial burden for one person to pay alone. This arrangement can continue for many years. Life is busy and it may never be the right moment to discuss the legal entitlements of each party.  So, the questions about what is fair and what is your legal entitlement may only arise when the relationship starts to break up.  

Do the contributions to the mortgage entitle you to an interest in the property even though you are not a registered owner?   The answer is that they may do, but it depends on the circumstances. 

The court will only grant you a share in the beneficial interest of the property if it finds that, at the point when you moved into the property, there was a) an agreement between you and the legal owner to share in the ownership of the property and b) that you acted to your detriment.  As partners in a happy relationship do not tend to confirm such agreements in writing it will be a matter of your evidence to the court as to what was said and whether the facts support your account.   The court may infer there was an agreement from the evidence before it.  Or the court could decide that, even though money was spent on the property, there was not sufficient evidence to infer such an agreement.  

Contributing to the mortgage substantially and over a long period would provide good evidence to support your claim that there was such an agreement.  And the payments themselves are detrimental acts.   So, you may have a good claim for a share in the beneficial interest.   The size of your interest will depend on the value of the property and the total contributions you made over the years.