Yes, it's a Sturmey "K" three-speed, with gear ratios of 59, 78 and 102 inches. The gear ratios were changed when he reached Lockerbie, to 55, 72 and 94 inches.
You can't see from the photos, but under magnification, it's possible to see that the Sturmey gear change quadrant plate and the pulley wheel have been drilled, presumably to save every ounce of weight. The bike is a Raleigh, a Clubman model, if I remember rightly. I don't know, but wouldn't be surprised if Rossiter's feat caused Raleigh to produce their "Record" model.
Rossiter rode the 800-odd miles in 2 days 13 hours 22 minutes, much of the time in heavy rain.
Neil Foddering
Weymouth, Dorset, England