When you see something as "official" as a photo mounted on a card with the typed-up caption, it's certainly tempting to a treat the caption as indisputable fact.
In this case, the claim in the caption that Pullin finished third in the BMCRC 600cc Sidecar Championship on a 3 1/2 hp (500cc) Douglas is verified by the article in the Motor Cycle on 13 Oct 1921. But was this photo taken on the day? Or maybe a month later? This is where it would help to know if the caption was typed up in October 1921, or sometime in the 1960s.
The Motor Cycle article about the BMCRC Championships in 1921 has specific comments about the Douglases that were on the track on the day: "... Pullin had fitted an ingeniously balanced air intake to his sports model Douglas. Bailey and Emerson (Douglases) used metal bridges to steady their engines to the centre of the middle frame tube."
Now I reckon that if Pullin's bike had twin carbs - a rare thing indeed in 1921 - the reporter would have mentioned it. The engine brace described was interesting, but the tech was at least a year old (
https://www.douglasmotorcycles.net/index.php?topic=7014.msg27469#msg27469 ). Pullin's air balance system was probably on the track for the first time, so worthy of mention, but twin carbs... surely worth noting!!
The photo below, from the Motor Cycle 10 Nov 1921, shows "C.G. Pullin, who won the 750 c.c. championship race on a 3 1/2 h.p. Sports Douglas at a speed of 76.49 m.p.h." The bike Pullin is sitting on in that photo is a single-carb Sports Douglas fitted with an early version of the air balance system: no air box, but the balance pipe is there between the carb and the fuel cap. Yet on that day in November, the article notes that "Pullin's Douglas had a large pressure box fitted around the air inlets of his two carburetters."
My guess is that the single-carb bike in photo below is the bike on which Pullin finished third in the BMCRC 600cc Sidecar Championship, and that the caption on the Brooklands photo is wrong.
Maybe someone has the riding numbers at the different Brooklands meets and can weigh in.
Leon