There's not much chance of finding an original reg. no and even less chance of being able to use it unless it happens to have found it's way onto the DVLA computer system (and then not get purged out).
In my experience of spending years trying to find a registration from chassis details, even if something is on their computer DVLA can't search by frame/engine/VIN numbers. (I've been told there is a separate database compiled for stolen and written-off vehicles that is searchable by frame/VIN, if you know someone in the police or insurance industry you might be able to get something from that, should your machine have found its way into the computer system and then been notified as stolen, or written off)
There are threads in the forum about cases where people have had barn-find bikes with registration plates and matching tax discs but they've had to be re-registered with age-related numbers because there has been no documentation/record to verify that the registration plates/tax discs actually belong with the frame number.
See here one of the (several) previous discussions on this subject. viewtopic.php?f=38&t=10134
'55 Huntmaster, '56 VH, ' 51 VH, '80 R100RT, '00 Sprint ST (but all those Ariel parts can only make one running bike...)