OK, I have experience of a very similar issue. I'll describe this first.
Land purchased was unregistered at LR in 2002. So first registration on transfer applied. LR butted the red line they show on the title plan against the neighbouring property that had been registered some 20 years earlier, using a very sketchy plan from deeds going back a century. There is no disagreement between neighbours about where physical boundary lies, and there are no obvious features on the ground to more precisely align the legal boundary to physical boundary. As you may know, LR do not warrant that boundaries on plans can be scaled from, they are called General Boundaries, unless a different surveying process is used to agree Exact Boundaries. New owner builds house and garage, with garage about one metre from agreed physical boundary. 7 years later LR write to say that using their aerial mapping techniques, garage shows as projecting into other plot by a triangle on a corner, about one metre by three metres.
LR seems to refuse to comment on the accuracy of their aerial scaling techniques but it seems likely they can now map accurately to within 0.5m, whereas in the past it was probably 2 metres accuracy. They do not seem to get alarmed unless a permanent structure straddles the boundary - which of course they track from updated aerial photos.
Ways of Resolution: there is no statute of period of limitation for this. It it will always cause a problem if your neighbour attempts to sell (because buying conveyancer will find it), and it will probably hinder you selling for the same reason.
You hold the whip hand, so you might wish to propose a solution.
In my opinion, (but this does not constitute advice), options are:
A deed of rectification where you just agree the legal boundary is in the wrong place, and agree to change it. No money changes hands but there is an LR fee.
A transfer of a piece of land of a described shape and size clearing the problem area of encroachment, for a consideration of £1 upwards. You could name your price, but don't get greedy.
A transfer of a larger piece of land whereby you give him the problem area in exchange for land of similar area somewhere else in his garden.
If you want to maintain relations, I'd go for the latter. It was no-one's fault, a bit like my case study above.