Yes it's a Beardmore Precision - a 350cc side valve Precision single from the early 1920s. The front fork has a leaf spring, but unlike some of its big brothers this one has a rigid rear end. It's not a lightweight though - the tank (which forms part of the frame) is made from very heavy gauge steel.
I worked on one of these a while back: when I started it I had trouble with fine rust particles from the tank blocking the jet. Just how do you shake this one and tip it upside down???
A very nice machine.
Leon