Further to my initial post, I have two further photos concerning the Home. One is of a couple of "Policemen" on motorcycle & sidecar, and the other is of a group of ladies from the Home, on said combination.
The Keystone cops aroused suspicion as the rider has comedy helmet and stripes. He does have a number on his collar and insignia on his shoulder, but no whistle chain. Plod in the sidecar has no insignia except on the helmet and that does not look like Invicta. Neither of their tunics are correctly fastened at the neck and the button spacings are different. KL registration was issued between May 1924 and September 1925, which tallys with the band brake on the front wheel, discontinued by BSA in 1926. The sidecar looks to have a BSA stand of arms logo on the door. There is a squirrel mascot on the sidecar, roughly under the rider's left hand. The man standing behind them has a peaked cap that looks to have Inspector on the front in script rather than capitals.
The photo of the Ladies on the sidecar gives names on the reverse, and a slightly different view of the sidecar. The rider is either my Mother or my Aunt - the jury is still out...
I estmate the date of these two photos at 1930, or just before.
Looking around the Homes website, the Railwaymen's Convalescent Home was next door, and there is a photo of some residents in what appears to be fancy dress, including Police uniforms. So I'm certain the Keystone Cops were just that.