Hi, regarding registration & lost commission number, if you know a friendly motor* dealer who HPi's to check cars
for history he can do it from the registration number. (*Scrap car dismantler who is end of vehicle life registered)
It rather depends if it has ever been on DVLA so if it has been off road before 1984 approx then it is unlikely.
If you check where it was registered ie the original dealer then somewhere there might be a ledger or files saved when the idiots ordered our licensing records destroyed. Usually start with a local archive. If you say where it was first registered I can check some records I have regarding places that exist, but many have simply vanished. while others have no room so actually binned the old saved records!!!!
There are also places like the KITHEAD TRUST that have some files, the snag is they might not respond as you do not have the magic number as I found out for a prewar MG in the same situation.
As Stuart says in recent times Heritage did say they can check from engine numbers .
Another possibility is the Coventry archives or the Standard Motor Club whose records might be what Mr Piggott used to supply.