NSALG is your best bet. They have a legal adviser. They also did a survey (10 years or more ago) on whether sites were statutory or not ... so they have info from that time for your site.
Without getting into legal minutiae, a rough explanation of the term statutory is that it indicates that there is a document, possibly a covenant, relating to the site that limits the use of the land to allotments. The fact that allotments may have been there for several hundred years does not, I am afraid, magically convey statutory status on them.
Good luck with the fight.