The Official copy of the register of Title, obtainable from the Land Registry has a section C Charges Registry. Its here that any remaining legal charges over the property will be listed. ie A Mortgage. If there are none listed then the Mortgage has been paid off and the Absolute Title of the property describes who it belongs to., in your case your parents.
If this is to apply for a visa (which it was in my case) as sponsor, the Land registry copy is acceptable. However it will do no harm to state somewhere that the property has no outstanding Mortgage and is owned outright.