As long as there is a clear vertical division and no cellars or projections which interfere with the grant of a freehold then it qualifies.
In simple terms freehold implies from the centre of the earth to the top of the sky so a cellar or room that crosses it cuses emblems with granting a freehold.
If they are refusing then have the matter determined at the LVT; counsels advice is not required, simply be represented by a local chartered surveyor that deals with house enfranchisement, who can give expert evidence for you.
Based on the information posted, I offer my thoughts.Any action you then take is your liability. While commending individual effort, there is no substitute for a thorough review of documents and facts by paid for professional advisers