.38 Special is too long for the cylinder, an the brass is a different OD; and the bullets are on the small side for accuracy.
Bullets should be .358, however I have had good success in the past using Hornady's .358 Cowboy Lead Round Nose bullets at 158 gr. While the Webly Enfied pistols are strong when in good condition; accuracy seems to suffer, so load on the light side. Also if you load hot, the trigger guard whacks (mine anyway) middle finger. With these bullets, I'm using HP38 powder, start at 2.0g and work your way up. 9mm dies work, but you will need a different shell holder.