I'm not sure, but the bike looks like a Excelsior Model9, what do you think?
About the only similarity with the Model 9 in the link that I can see would be the headlamp bracket, which probably came from the headlamp manufacturer (Lucas?) so could have been supplied to many different motorcycle manufacturers?
Your grandfather's bike looks more like a sidevalve model rather than overhead valve, judging by the position of the exhaust pipe?
Also there's no handchange lever, and the forks and brakes are different to the M9?
Using some photo enhancement, it may possibly have an "A" (BSA maybe?) on the tank, but I couldn't say for sure?