That's a very easy one Nigel,
It's an L series Matchless. It is the great grandaddy of all the so called 'Heavyweight single' Matchless and later on AJS.
It started out as a 350 (69x93 bore & stroke) and then was bored out to 82,5mm to make the 500. Matchless then kept updating it year by year, making an ohv version of the 350 and later the 500 and kept on updating it until the factory folded in the 60's. By then about all that was left of the original engine was the gudgeon pin and little end bush. Once you know the code you can follow the parts numbers for these throughout all the years of production.
I'll have a careful look at the photo and see if I can be a bit more precise as to the exact model in the series and the year.
Cheers, Bob