Adverse possession question

We are sale agreed on a house in an estate. On the folio map, part of the driveway connecting it to the public path/road is owned by the estate and not by the property. It is 20 years old and the current owners are there more than 12 years. No planning ever submitted on the property so it is original and there are walls on the edge of the property enclosing this 'no man's land'. We have been advised that as the builder is in receivership it's highly unlikely he can sign over this plot to the property and that the sellers will have to apply for adverse possession as the bank is likely to take issue with a mortgage for a flawed title.

Does adverse possession have to be done by the people who are in situ more than the 12 years? Or could we take possession and do it as the driveway has always been like that? We are gutted to have the sale delayed, does anybody know if adverse possession is any quicker/easier if it's part of the property and not an extra plot behind the property etc. that nobody owns?