Kees, as usual has the best answer <g>.
Much of this material name thing depends on whether you are talking today or 70 years ago.
Today much of the canvas seen is cotton or heavy in cotton fibers. In the old days and even today "canvas" typically means a heavy weight cloth for sails, tarps or webbing. it could have been made from cotton, linen, or hemp. Some strops were even made from silk.
Canvas (cotton, linen, hemp, etc...) cloth can be found but once cut into strips you have to deal with the cut edges. The best material for ease of use will be webbing which is harder to find.
I can supply a coarse cotton "canvas" webbing, a smooth, hard finish cotton "canvas" or genuine linen in a smooth thin weave. I'm working with a mill now to supply hemp such as Dovo uses.
You will commponly see the cloth side of a strop called "canvas" or "linen" with no regard to it's actual fiber content....today it is simply a generic name that is more often than not, inaccurate.
While not exactly the same as old day materials I specifiy mine as cotton or linen based on actual fiber content, Keith's wool felt, again tells you what is really used.
Once my remodeling is done I'd be glad to supply "cloth" webbing if you need it.
Tony