My dad said he thought that someone on the side of the family from where we believe the photographs came, used to work for Sunbeam and he wondered if that was a clue.
Sunbeam started out making bicycles but when they did begin to manufacture motorcycles, they gained a reputation for quality and did well in the famous TT races on the Isle of Man.
Another proposal was that the bike was a James, dating from around 1921- 27, because of its chain drive and not the earlier belt drive. It was suggested that this actual bike might have been modified in some way.
To settle the matter I contacted the National Motorcycle Museum in Birmingham to ask for their thoughts. James Hewing very kindly responded to my email and identified the bike as an Royal Enfield 500c, from around 1927.
Interestingly, while watching the new BBC drama, The Crimson Field, about a field hospital in WW1, one of the characters arrived on a motorcycle which looked suspiciously like the one above with its distinct box-like petrol tank. Whoever chose the 'props' obviously did their homework. Apparently Enfield supplied the British War Department with a large number of motorcycles in 1914.
But having identified the bike, I'm still no further on in identifying the lady sitting astride it. Any suggestions?