I restored a 1972 car (not a Triumph but an MG, OK I'll get 'me coat!) for which I didn't have the V5 or registration number. The process I
followed was:
1. I bought a Heritage Certificate based on the vehicle chassis number see
http://www.heritage-motor-centre.co.uk/archive/cer....
2. I got the car insured based on the chassis number
3. After completing the restoration I had the car Mot'd on the chassis number.
4. I went to my local DVLA office ( I live in North London so for me it is at Stanmore). They accepted the Heritage certificate as proof of
year. I had to take the car to their inspector to prove that it really existed and the numbers were true. They then issued me with an age
related registration number ( a K plate) and as it had been previously registered they made no charge. They also issued a tax disc on the
spot.
5. I updated the insurance information, bought some new number plates based on the document provided by the DVLA.
6. V5C arrived by post a couple of weeks later.
I was suprised at how easy it was. I never di find out what the original registration was.