DVLA do offer a facility to investigate the history of a car if you give them a good enough reason! They are only likely to consent to do it for a car registered in the name of a UK resident with the car also registered in UK. You in Canada & car in Canada sounds unlikely you will get anywhere. The whole searching for past history is a disgusting situation caused by idiots in the civil service, who were totally unsympathetic & ignorant to our motoring heritage.
The major problem is that when the centralised records were set up in the 1970's some half witted civil servants decided that if any vehicle had not been taxed on the road during the previous 2 to 5 years then they could safely destroy all the records held by the vehicle offices scattered around the UK. Luckily a lot of local archivists rescued records & many did not find the way to Swansea and so survived, about 50% ended up at various storage sites in South Wales & ultimately were destroyed.
It seems since that even early issues of computer registrations done in the 1980s are now not recognised. The whole place is a general nightmare & it is unsafe to believe much that comes from them regarding history.
Many records from major offices such as London, Middlesex, & other towns & cities had either been destroyed during WW2 bombing raids or destroyed before the DVLA was set up.
From my own experience the DVLA do not seem to have anything totally accurate after about 1960, even post 1970 is inaccurate to what I already know!
Some replies I had such as for several Triumph TR2 & 3 gave the 2nd or 3rd owners as the only owner, & date of registration was wrong.
In another case my Maserati records missed out owners for the first 2 years.
I would not have much hope of success. I think it rather depends if the car has continuous use and not laid up off road untaxed,- if there is a gap in taxed records or many owners that then filled up the RF60 older registration book then it seems unlikely they have any record.
Registration books were replaced & renewed & they never bothered recording everything. When they requested people to send in & claim their vehicles registrations they expected a few thousand and were snowed under with tens of thousands.
Depending where it was registered you might get help from various archives & others such as the Kithead trust who hold records that fortunately never reached Swansea.