The Webley and the .38 S&W pre-date the .38 Special plus I believe the Webley would require a longer cylinder to safely chamber the .38 Special. The Webley dates from the late 1870s and would have been distributed throughout the Empire long before the .38 Special came along...and to inject another caliber into the logistical chain around the world would have been difficult so I think the Brits kept the .38 Short and Weak for logistical simplicity, regardless of what revolver they purchased as needed. Given that most armies don't consider a handgun a primary weapon it was probably a reasonable decision from their point of view.
As far as the M1 Carbine caliber goes...it was expected to be a secondary arm for troops not engaged in front-line combat...engineers, headquarters personnel, etc., that could do better with a carbine rather than a handgun. I've also read that part of the caliber decision was based upon barrel manufacturing technology was already centered upon the .30 caliber diameter. The military gave gun companies a list of qualifications and they responded with the guns and ammunition that met the requirements. That doesn't mean the requirements always make sense or justifiable but it's what the military demanded and the contractors met.