If it's in one of your books, you're way ahead of me.
I've got the M12 in one of mine, plus photo, but all it says about the M13 is:
"The one-off M13 Hobby, a tiny single-seater built for the 1937 Kings' Cup race, had a 140hp Gipsy Major 2 engine. Trouble with the retractable landing gear prevented it from competing and it was sold eventually to the RAE for full-scale wind tunnel tests".