Bisby in real life George Formby was a motorcycle enthusiast and I believe rode Norton, in the film he called himself George Shuttleworth which is why the bike he supposedly built was called the Shuttleworth Snap, I think it was built around a Triumph Model P. The race bikes doing the most winning around that time were the Marston Sunbeam so Sunbeam became Rainbow in the movie.
Charlie on second look the forks are Triumph like so a pre-unit twin from Triumph it could well be?