SW38:
Your gun is a pre-Victory model .38/200 British Service Revolver. The earliest serial number I know of was 685147 range, shipped 3rd May 1940 to the Union of South Africa. By the 12th April 1941 S&W were shipping guns in the 860,000 range.
There is no model number because model numbers were not introduced until 1957, the numbers under the cylinder yoke are assembly numbers, used to track parts in the factory. They have no meaning after the gun is completed, only the serial number was recorded.
The S prefix was introduced in 1944 Some US service guns were retrofitted with the new hammer block and stamped with an S on the left upper frame. Yours is not a US service gun so it will not be stamped.
There are no US Property marks because it predates the Lend Lease agreement and was a private contract gun, either for Her Majesty's govt. or for an exporter. The lanyard loop was a requirement of the British contract guns, the order was for 5 inch barrels, but after Dunkirk they would take whatever was available as the BEF had abandoned its arms during the evacuation.
The finish is probably Black Magic, a proprietary rust bluing that S&W purchased from another company when it could not keep up with demand using its Carbonia bluing. The Black Magic finish appears to be parkerized when worn and is also relatively thin.
You are correct, it is a 5 screw gun.
For a $50 fee you can get a factory letter stating the date the gun left the factory, where it was shipped to and the original configuration.
http://www.smith-wesson.com/webapp/...4_750001_750051_757825_-1_757814_757812_image
Edit: Caliber is .38 S&W. There is a different .38 Sort Colt that is still produced for the Cowboy competition crowd.
TWMaster:
The above info applies to your gun as well.
The patent dates are correct for a .38 Military & Police Model of 1905 4th Change, which the British Service Revolver was based on.
Usually S&W stamped a B before the serial number under the barrel on its pre-war guns. Have another look and see if it could be a B. If it's an O it may refer to the wartime finish, I've never found out whether B stood for blued or for barrel.
The P may be for Proof, some guns were proofed at the factory during the war and marked with a P.
You are correct about the grips, they are post 1968 Magna grips.
The X is marking was used before and after the caliber designation.