I had an article for loading for just such a critter in The Fouling Shot No. 241 and a followup in No.242. If your 1930s Colt is dimensioned like mine, soft .358 bullets will work just fine with 2.5 grains of Bullseye.
To save you looking it up, here's the data:
Table 1 – Comparison of weight and dimensions Colt vs. Webley
Webley Mark IV .380 (1950) Colt Police Positive .38 Colt NP (1930)
Barrel length: 4” 4”
Overall Length: 10.1” 9.5”
Height: 5.1” 4.5”
Weight: 26.5 ozs. 20 ozs.
Cylinder Diameter: 1.45” 1.40”
Cylinder Length: 1.30” 1.30”
Cylinder Throats: .362 .359
Cylinder Gap: 0.005PASS/0.006HOLD 0.005PASS/0.006HOLD
Barrel bore/groove: .355/.362 .344/.354
Table 2 - Velocity Comparisons Webley & Scott .380 Mark IV vs. .38 Colt New Police Positive
Ammunition: Webley Mark IV Colt Police Positive
Fiocchi 146-grain LRN factory load 750 fps, 19 Sd 794 fps, 14 Sd
Accurate 36-125T, 2.7 grs. Bullseye 761 fps, 10 Sd 803 fps, 10 Sd
“ “ “, 3.0 grs. Bullseye 837 fps, 16 Sd 883 fps, 9 Sd
Accurate 155D-146-gr.HP 3.0 Bullseye 794 fps, 15 Sd 852 fps, 12 Sd
Accurate 36-155D, 2.1 grs. Bullseye 640 fps, 8 Sd 671 fps, 11 Sd
“ “ “, 2.5 grs. Bullseye 710 fps, 16 Sd 756 fps, 11 Sd
Accurate 36-178D, 2.1 grs. Bullseye 595 fps, 10 Sd 601 fps, 18 Sd
Ideal 195-grain #358430 1.7 Bullseye 513 fps, 11 Sd Would not chamber in Colt
Accurate 36-201D, 2.1 grs. Bullseye 601 fps, 12 Sd 612 fps, 20 Sd
NOE 201-grain Mk2, 2.1 grs. Bullseye 609 fps, 12 Sd 629, fps 15 Sd
73 de KE4SKY In Home Mix We Trust From the Home of Ed's Red in "Almost Heaven" West Virginia