Land law co-ownership

Okay, lets say the title to a house is registered in x's sole name, even though y contributed 20% of the purchase price to the property from their savings and lived there with x. Does this mean that there can be no express trust declaration of the proportional equitable interest (tenancy in common) as we are told that the legal ownership is only in X's name or does this only relate to the legal joint tenancy and Y's beneficial interest could still be mentioned elsewhere? Finally, what are the co-ownership implications and what of Y's interest if X's tries to sell the house without Y's knowledge? Moreover, lets say y is in hospital for 2weeks so isn't present but has belongings in the house? The seller C has lots of money and doesn't need a mortgage, what are the implications of this? What is some seminal and helpful case law?
Thanks, A.