That was a BSA M20.
They were used by the British Army
and US Army. That one doesn't have the US markings, but many did. They were primarily used by the Army Air Corps in England during WWII, and were supplied by the Brits to the Americans staioned there. Many saw service in North Africa as well.
I have two customers who own M20's. They are really neat bikes and still quite rideable.
Here is a good link with some info:
http://home.quicknet.nl/qn/prive/ahum/