it would be quite an undertaking. as I understand it .442 webley has a bullet diameter of .440 however most of the modern bullets available for 44 special and 44 magnum are actually .429 diameter, you would probably have to cast your own bullets and a .440 bullet cast would be very hard to find I'd wager. then you would have to cut fashion your own casings, probably out of 44 special or 44 magnum, depending on what you can get cheaper. there is always a huge gamble when you buy a gun in an obsolete cartridge and sometimes it just become more bother to try and fire it than it is to just put the gun in a pretty glass case and admire it.
the link to buffalo arms is no longer active as they have discontinued their 44 webley ammo line however they do still have brass
for 44 bulldog, a shortened, less potent cartridge compatible with 44 webley. as well as bullet molds
that may fit, though you may also have to run them through a sizer.
your biggest hurdle is going to be finding the proper amount of black powder to load into them without jeopardizing the gun.