Hi Andy,
Yes indeed it is a Douglas - a 2 3/4 h.p. (350cc) from around 1915. I say "around" because in wartime the specification probably got messed around a bit - if not in production then through repairs where there was a degree of "mix-and-match". Post 1914 features are the rear stand pivot on a lug below the rear axle (on the earlier bikes the pivot was on the chain stay in front to the axle) and the one-piece timing cover (earlier motors have a two-piece affair, with the upper cover stepped inboard a little). The front forks are the early pattern with the kink in the front bracing tubes. Around 1915-16 there were new forks with straight front tube, but the early type were apparently still used on some machines. The CAV magneto is unusual. Great photo!
Leon