The only real inconvenience in reloading for the .38 S&W can be in finding bullets of the proper diameter. Standard commercial .38 Spl./.357 Mag cast bullets are usually sized at 0.357 or 0.358" and the nominal size for the .38 S&W is 0.363 - 0.364".
Other components are pretty easy to come by, as are dies, data, etc. Starline makes brass and it's reasonably priced. It's entirely possible that there're commercial casting outfits who make slugs sized for the .38 S&W, although they might be a special order item. There may also be a minimum order, which would be understandable.
Midway lists at least a couple of different brands of factory ammo. It costs a bit more than .38 Spl., but it isn't (or at least wasn't) hideously expensive.
If you decide to reload, just remember that while the H&R's were well-made revolvers the design isn't as robust as the Webley nor as strong as the solid frame Smiths. It'd probably be a good policy to stick with the starting loads and bullets of 150 gr. or less.