Jointly owned property can be owned only in two ways - joint tenancy and tenancy in common.
If it is a joint tenancy, each owns the whole, there is no share or division. When one dies the survivor still owns the whole.
A tenancy in common is different - each owns a share that may or may not be equal. So two people could own it 50/50, 70/30 or however has been decided between them. Each can leave their share to whomever they want to in their will, or even sell their share at any time.
You can tell how a property is owned by looking at the Title Register (downloadable from �3 from the Land Registry) If it just shows the names and addresses of the owners it is a joint tenancy. If the names are followed by a restriction it is a tenancy in common.
A Trust Deed is only relevant to a Tenancy in Common and should specify how the share each person owns either as a per centage or a fixed sum.
So, if it is a joint tenancy it matters not a jot who paid in what - both are entitled to an equal share of the equity.
If it is a tenancy in common there should be a trust deed. If there is no trust deed there will be an assumption of equality.
Of course, if one of the party is adamant he or she is entitled to a larger share he can go to court in certain circumstances