Hi Brewster. If you have reason to believe that your dad owned a 500cc Speed Twin, then I would say that the bike in the picture is probably it. Difficult to identify it conclusively but my best guess is that it is a pre-unit 5T (with separate engine and gearbox) early/mid '50s version with swinging arm rear suspension - as opposed to a rigid frame and sprung saddle as per the earlier models and the later unit construction version (5TA - I had a 1960 version for my sins!) with the 'bathtub' rear wheel/frame covers and full width front brake. A similar 6T 650cc bike was also available around that time, which makes accurate identification a bit difficult. All the above is from memory, so please forgive any minor inaccuracies. As I believe most folk herein would agree ... I am trying!
Not a great photo but looks like early speed twin 500cc, try looking at bottom of barrels of bike pavement side, what does it say, If there's an engine number there that would help dating a lot Good luck.
All the above information has narrowed it down. My brother remembers my Dad saying he wanted a Tiger but they didn't have one so went for this one. It would also be mid 50's. The little girl is my cousin and proved next to useless! Thanks again everyone.
Just checked DVLA database , no record of that number but that doesn't mean it's not in a shed somewhere https://vehicleenquiry.service.gov.uk
