Those images help.
I agree - - it is a WW-II vintage Victory Model version of the standard Military & Police or Hand Ejector revolver.
I'd like to see a photo of the entire right side of the barrel.
S&W supplied these revolvers in both .38 Special and .38 S&W caliber (the British called it the .380/200, though most of their military ammo was loaded with a jacketed bullet of about 174 grs.) Most of the ones sent to Britain had the five-inch barrel, and, even at the height of the wartime emergency, were British proofed and so marked. You are so detailed in your accounting and illustration of the markings, I doubt this is a British service S&W.
Most of the four-inch guns were in .38 SPL and went to the Navy for aviation use. I imagine this particular item is in .38 SPL, due to what you correctly figure is the Ordnance flaming bomb. The lanyard loop stud had been ground off prior to the refinishing, and the S&W Magna style stocks are a replacement. Many, but not all, of the US revolvers were stamped "U. S. Property" along the top of the frame.
Such refinished revolvers may be excellent shooters, but many suffered in the process. I suggest you take it through the procedure Jim March describes in his excellent article, "Buying a New Revolver." Go to the menu at the top of this page, in the center of the top line, and click "Library." The article is at or near the bottom of the Contents list. If the old revolver passes, it should be okay to shoot with all standard loads. While these were good, solid firearms, I'd be a little hesitant to shoot any .38 Special loads marked "+P" through it.
Best of luck,
Johnny