I guess the first step is to contact the DVLA, this site looks useful:
Getting vehicle information from the DVLA About 25 years ago I wrote to them requesting details of a 1969 MGB I owned. They replied with an impressive collection of photostats of all the original documents including the log books, which they then held on microfilm.
I'm afraid I have no idea what you get nowadays, hopefully someone who has tried it more recently will reply.
~iw