Unregistered piece of ground. Land registry/mortgage/conveyancing related

Within my 'plot' which my house sits on there is an unregistered piece of land. It is probably the size of a snooker table on plan and is surrounded by land which I own. It came about from buying up a number of gardens to build the house where I am. It looks like years ago there was a mis-measurement or mistake somewhere which resulted in this piece being unregistered. My conveyancer said it was obvious that this was the case. I did get a sworn document off the previous owner that in over 12 years she had exclusive access and no challenges etc etc.

At the time my conveyancer gave me the option of holding onto this document, or applying for adverse possession. She said it could all be tidied up if and when I was to sell. I'm just wondering now if it would make more sense to apply for adverse possession or if it makes no difference. I wouldn't want to find myself in future having to sell up then the sale falling through due to the unregistered piece of ground. Likewise I wouldn't want to claim adverse possession and find that doing that creates the same problems in future should I need to sell?! I remember at the time convincing myself that the sworn document was fine and it would be better to deal with if and when I sell up, perhaps with an indemnity. Particularly with the advice that the reason for the unregistered title appeared obvious, as opposed to someone pinching half their neighbours garden.

I just want to feel what the collective opinion is particularly from a conveyancing/mortgage point of view on the best course of action. I do know that messing around with the title would exclude any sale for the following 6 months but that is not a concern of mine.

Thanks.