Yes, I agree with Leon. I have my blurb on the Royal Enfield Expanding Band Type of Two-speed Gear sitting in front of me as I write. To quote,
"The engine shaft carries two pinions, and two chains run to the countershaft. Since the engine sprockets are if different sizes, the gear ratio will be higher when the drive is taken through the chain running over the larger one, than when it is taken through the smaller. The Enfield gear consists of two sprockets each having inside it a clutch, with the selector mechanism by means of which either clutch can be brought in to action, locking the sprocket to the shaft which carries the sprocket for the back chain."
On some models the change was effected by a rocking foot pedal, others had a hand change.
As Leo says Royal Enfield fitted these just about across the range and there are minor differences. The heavier versions had roller races on the main shaft bearings where the lighter versions used ball races. They are easy to tell apart when you know what to look for.
Currently there is a bloke on Facebook trying to sell a 1926 2 speed Royal Enfield two stroke minus both the original engine and your two speed set up. You'd have a flying start on sorting out a nice little vintage bike.
Cheers,