Definitely not .303 ... a .303 cartridge would slide right through the bore of a Snider-Enfield and fall out the muzzle!
(Admittedly, late 19th Century arms and equipment are likely more my cup of tea than most here ...)
As I mentioned, the bandoliers in the photo are Pattern 1882 Mounted Infantry bandoliers, which were actually designed for use with the honkin' big bottlenecked .577/.450 Martini-Henry cartridge ... but they also work just fine with the .577 Snider-Enfield cartridge, which has the same body and rim diameter. (This I know from personal experience, as I own and shoot several Snider-Enfield and Martini-Henry rifles ... and have a very nice reproduction P'82 bandolier amongst my kit.)
"List of Changes" entry:
The first official .303 bandolier was the Pattern 1888 - which was essentially the same design as the P'82, but with downsized cartridge tubes - introduced for use with the Lee-Metford rifle adopted that year. That rifle, and the Lee-Enfield variant of it were, of course, still charged one round at a time, so this sort of bandolier remained desireable.
To move this thread properly back into the 20th Century (
) the Pattern 1903 bandolier equipment which most folks here would likely be familiar with (i.e. with the pocketed leather bandoliers accomodating two 5-round chargers in each pocket) was introduced for use with the new S.M.L.E. That equipment had two bandolier designs - one with a total of nine pockets (five at the front and four at the back) for mounted services, in addition to the standard bandolier with five pockets (in the front) for infantry, who also had waistbelt mounted pouches ...