To me a barn find is totally different as somebody at some point has obviously put the car away rather than just dumping it in a layby/roadside/car park or any other public area and who said barn finds are free to the next owner? Most barn finds are usually sold on (yes, people actually pay money for them) because the current owner may have had a change of plans, they may have died so the wife or husband wants to get rid of it or many other reasons but very rarely are they just given away. Fuck me if you were allowed to just help yourself to old vehicles found in barns there'd be a lot of farmers missing their tractors.
I would have thought the most common sense way to get an answer to the OP's question would have been for him to ring the DVLA in the first place rather than believe 30 odd different suggestions on a forum.