The .44 Webley (.442RIC) cartridge case can be made from .44 magnum, .44 Special or .44 Russian Brass. The process according to Donnelly in The Handloaders Manual of Cartridge Conversions requires shortening the case to 0.690", reducing the rim diameter and thinning the rim.
.44 Bulldodg cartridge cases are 0.57" in length with all other dimensions the same as the .44 Webley and therefore could be used in the Webley clhamber.
Bullet diameter for the .44 Webley is 0.436. The easiest way to produce a shootable bullet is to minie' a 0.429-0.430 bullet by drilling a 3/8" hole, about 1/4" deep in the center of the bullet to create a skirt that will expand and engage the rifling upon firing.
The original loading for the .44 Webley per Cartriddges Of The World was 15 to 19 grains of Black Powder. Donnelly in the above referenced work suggests 4.0 grains of Bullseye with a 200 grain bullet. I personally feel this load is EXCESSIVE and DANGEROUS in pistols of unknown quality. A charge of 1.5 to 1.8 grains of Bullseye would be more in line with Black Powder pressures. Another smokeless powder that will produce acceptable pressure levels is Trail Boss by IMR. I have not personally worked with Trail Boss but IMR loading data indicates that light charges will produce low pressures in obsolete pistol cartridges.