They were first introduced in 1903, and up until 1973 you got one from your local council. In 1973 the issuing of driving licences was taken over by DVLA and since then the records have been computerised. So unless who you're after still had a driving licence in 1973, it's unlikely to be on DVLA files. Nor sure if they'd release such data anyway.
National Archives web site is worth searching in case they have anything further. http://www.nationalarchives.gov.uk