Hello Katy - land doesn't
'become unregistered' so it seems likely that when the property was first registered whoever applied either didn't include it in the application for some reason. Perhaps because they didn't realise or more likely they didn't have the deeds to prove ownership
The first thing to do would be to look at whatever paperwork you inherited to see if it includes the original deeds/documents. They would have been returned to the applicant at the time of first registration.
It's possible you have already done that though as you then refer to trying to claim the land.
Our PG 5 explains more re applying to register such a claim. It's unclear how your neighbour might have a counter-claim based on what you have stated as it's presumably quite clear it's your patio and part of your property. But do seek legal advice as well to clarify/confirm the legal requirements needed to support any future application to register your claim.