Upon further review, 1903 Rex is a much closer match:
OBH, thank you - after nearly two years of searching I've had both questions answered within a few days of each other. Thanks so much for taking the time to track this down. It clearly is a Rex, there's no doubt about it, which begs the question, why does the original photo have a small shield on the petrol take which reads 'Irvine Imperial' Perhaps the bike was purchased wholesale from Rex and marketed under a retailer/agent's brand name ?
All the best,