Hi Sarah - I am sorry to read of your loss.
If they bought 50+ years ago then it's unlikely to be registered. And if the original deeds/documents can't be found then an application to register for the first time is required
If they were joint owners then you will need probate for your late Mother and a death certificate for your late Father. The executor can then transfer the ownership to the beneficiary as appropriate. And that transfer will trigger the need to then register the property.
HMLR Guide Page · HM Land Registry explains what's required on both counts.
If you are happy to share the postal address of the property I can check to confirm it is unregistered