As far as I'm aware, the black sprung saddles on British motorcycles which first appeared during the late 1920s were never leather-covered, unlike the brown leather pan saddles fitted to many true vintage motorcycles.
They were covered with a leathercloth, in most cases the 'Rexine' which Steve refers to. This was a linseed-based covering over a canvas backing. It was relatively 'hard' to the touch. Not soft and 'warm' like modern vinyls. Unfortunately, ICI appear to have stopped producing the upholstery grades during the 1960s, although specialist bookbinders have access to some very thin examples.
The non-availability of 'Rexine' is one of the greatest barriers to authenticity in the restoration of a 'post-vintage' motorcycle. New Old Stock WD covers (from the 1950s) do appear from time to time but they're not common and any original saddles are likely to be worn and fragile.
There are some harder grades of vinyl as used by car upholsterers with a more correct look than the mass-produced covers. Additionally, I've never seen an original example with that 90° corner to the back edge - although common on replicas, they always look wrong.
I don't believe that there has ever been documented evidence of the supply of canvas seat covers for motorcycles. The general view is that they were fitted as gunner's seats in some self-propelled guns.