Adverse possession - does applicant have to have known he was not the owner of the land?

My parents bought a house 40 + years ago, when the land was not registered.  I have inherited the property and wish to apply for first registration, but have discovered that a small piece of the garden was not transferred to my parents.  This happened because the conveyance did not include a plan; the property was simply described as the dwelling house and messuage etc known as (address).  It turns out that, when their vendor had bought the property, that conveyance had contained a plan.  This excluded a part of land that my parents believed was within their garden.  Obviously the vendor could not sell them land that he did not own.

The land had been bought and sold several times before the vendors bought it, often as part of a larger parcel.  The owner of the excluded section is not known.

Given that the original legal firm seems to have provided a sloppy service, I don’t wish to go to them for advice.

i would like to apply for adverse possession.  I’m confident we can show that my parents treated the land in question as their own throughout the full time they occupied the house.

However, does it matter that my parents apparently did not know that they did not own the land when they were “adversely possessing” it?

 

James - the law is a complex one re such claims so whilst I understand the 'sloppy' comment please do seek legal advice if only with regards the specific Q you ask and how you, as their beneficiary, might be able to make a legal claim. 
I mention the second point as it reads as if it was your parents who have adversely possessed the land but who are now sadly deceased. And as such that's a much bigger Q to have legally answered than the one you posted.
Our PG 5 explains the registration requirements but those come after the legal ones - Practice guide 5: adverse possession of (1) unregistered land and (2) registered land where a right to be registered was acquired before 13 October 2003 - GOV.UK