I'm guessing that there is no paperwork; therefore, there is no number to go by? Unfortunately, the commission number won't appear anywhere else on the car. Worst case scenario, though, is that you can contact British Motor Industry Heritage Trust for a build certificate. They usually can search by a body number and/or engine number (if you're fairly sure that it's the original engine) for a few dollars more than a regular search would cost. You'd then hopefully have the commission number and could get a new plate stamped up as well as register the car.
http://www.heritage-motor-centre.co.uk/archive/certificate_index.html