Hi Andrea - applying to register land for the first time where the deeds have been lost/destroyed or by way of a claim (adverse possession) is not as complex as many might think. It relies largely on the 'facts' that can be presented and whilst putting those facts together may take some effort/time it's invariably possible to do
Clearly the sad loss of your parents adds to the effort/time perhaps needed to put those facts together also
Our PGs 2 and 5 explain how each type of application can be made
First registration of title if deeds are lost or destroyed (PG2) - GOV.UK and
Adverse possession of (1) unregistered land and (2) registered land where a right to be registered was acquired before 13 October 2003 (PG5) - GOV.UK