Boundary line - informal agreement with neighbour

Hi -- 
Hoping for some guidance here. My parents bought their house 40 years ago, and they inherited a large tin shed built within the garden (shown on the title plan), with a small (maybe 5m squared) piece of land behind the shed (inaccessible to my parents) being used by the next-door neighbours as part of their garden (I'll refer to this as the "Contested Plot").

My parents have recently had the shed demolished (to be replaced with a different construction), and needed to arrange for a new fence to be erected along the boundary line (the fence is their responsibility).

The neighbour initially claimed rights of adverse possession based on use of the Contested Plot for a period of time. My parents did not want to enter into a protracted dispute and have reached agreement with the neighbour to erect a fence dividing the two gardens in a manner whereby the neighbour gains some (but not all) of the Contested Plot. 

The fence is now up, but there has been no agreement in writing with the neighbour (even informally). My question is where this leaves the ownership of the Contested Plot. The title plan - though of course not necessarily precisely to scale - will show that my parents' land includes the Contested Plot, but the reality is that the neighbour has now informally acquired rights to use part of that plot.

Would my parents be well-advised to arrange for an official redrawing of the title plot to document the agreement to divide the Contested Plot between the parties, or would the combination of (a) a general acceptance that boundary lines on title plans are somewhat loose and (b) the fact of the existence of the fence mean that this is not a worthwhile exercise?

Thanks in advance for any insights.

Hi Jo - it reads as if the contested plot and registered extents are large enough to be 'seen' on the title plan. That suggests to me that if they have in effect split the contested plot the 'best' option would be to transfer the part to the neighbours 
Registering land or property with HM Land Registry: Change the registered owner name - GOV.UK
Whilst general boundaries can be described as 'loose' they aren't so loose that a significant change in position doesn't need to be dealt with effectively. Likewise a boundary agreement or determined boundary won't formalise a significant change of the type you have described.
Leaving things as described is likely to pose an issue for your parents or the neighbours should they come to sell/remortgage for example if a buyer/lender spots the boundary 'difference' for example

Thanks, Adam. That's very helpful. In a case like this, what would be the process for designating and documenting the land carved out of my parents' title and to be transferred to the neighbour? (i.e. to be identified on the plan annexed to the TP1)

Jo - that's a matter for your parents/the neighbour to decide upon as it's their 'process' to decide what land is being transferred.
Our PG 40 sup 2 explains what 'quality' of plan is needed to define the transferred extent - Preparing plans for HM Land Registry applications (PG40s2) - GOV.UK