Unregistered strip between registered holdings, best way to proceed?

Two separate registered holdings, lets call them A and B. Our holding A was purchased in 1982 and was registered just last week. The boundary line between A & B has never changed in 42 years.  Neighbours holding B last sold in mid 2000's.

Between the two holdings is a small triangular strip, enjoyed by A, that remains unregistered. Due to an error in the 1982 tiny title plan the fence line was shown incorrectly and was never picked up.  We (A) have enjoyed the use of this land up to Holding B all these years.  Owner of both holdings agree that the B title plan is correct and a boundary agreement has been prepared and signed by all parties.  There are no third party owners and we have title deeds from when both A & B were a single holding prior to 1982 sale.

We require the title plan of the newly registered holding A to be updated in line with the boundary agreement.
What would be the best way to proceed please?  I am aware that adverse possession may well succeed but is there a simpler route?  Form DB supported by the boundary agreement or form AP1 a request to change the register of A supported by the boundary agreement (with or without form DB?)  What documentary title proof would LR require?

Your guidance would be much appreciated.

Michael - if the land is unregistered a boundary agreement/determined boundary is not going to suddenly cause it to be registered and included in a title for example.
The two options are usually either an application to correct the 'error' which would include supporting evidence as appropriate for example an original deed showing the land was included; or
An application for adverse possession as you mention

Thank you Adam. Correcting the error - What application process would I follow, is there a form or procedure to start the ball rolling?

Thanks

Michael - if you think that there was a registration error then you would use the contact form to report it
Public guidance: dealing with land and property - GOV.UK