There is no way either the Webley Service Mk II or the Mk III would have been bought as trainers by the military. Even with the cheaper ammo they would be far too expensive for recruits to practice with, and too dissimilar to the service rifles. Maybe Armed Forces target shooters might have bought them for their club use, but I really doubt they would have been used for practice. A Webley Service Mk II cost about £500 in real terms at the end of the 1930s. The SMLE in .22 rimfire would be far cheaper.
http://rifleman.org.uk/Enfield_Rifle...RF_Mk.III.html