Something like this should have been discovered when you were buying the property. A boundary survey would have exposed it.
It sounds like your solicitor may be doing a Section 49 application for you. You may not have the required 12 years yourself but you can rely on the time the previous owner occuppied the land also. These types of applications are notoriously slow (although they have become quicker in recently) and are costly. Like all government departments if you get the right person and ask nicely for it to be moved on a little quicker, explaining your predicament, the Land Registry will usually assist.