At that SN, it would probably have shipped in early 1941, just when S&W wartime production was ramping up heavily. The lanyard loop would indicate military intent, and in fact, there was probably very little civilian M&P production at that time, and none in .38 S&W. And that caliber would certainly indicate a British military order. Other than the caliber and lanyard loop, it is a civilian Model 1905 M&P, 4th change, and would have had medallioned checkered wood grips as pictured, and a commercial blued finish. A 6" barrel length is not unknown, but the Brits preferred 5". They took what they could get. It is not very likely that it was sold into the US commercial market, and it is also possible that, during that period, it would have gone to Great Britain unmarked, and may not have received any markings there, either. Things were a little hectic on the island at that time, what with a German invasion still possible. Getting guns in the hands of the troops quickly was the top priority.
M&Ps disposed of by the Brits into the commercial markets after the war were usually proof tested and are so marked. But there are many ways by which these revolvers found their way back over here that were outside official channels. A nice pre-Victory which has not been molested (i.e., rechambered to .38 Special or refinished) is a good find.