This gun has undergone some major modifications during its life.
From the serial number you describe (V + four digits), we can say that was shipped in 1942. The proof marks and abbreviations indicate that it was in service in Britain. It probably (but not certainly) originally chambered the .38/200 round, which is the standard military chambering for commonwealth countries at the time. The .38 Special is a different round, slightly more powerful, that was the chambering for the American versions of this revolver.
The gun was originally a fixed sight revolver, but was converted to a target model by the addition of adjustable rear sight and taller front sight blade on a ramped base. The base resembles but is not identical to front sights installed on converted wartime revolvers by Parker-Hale in Great Britain after the war.
I can't see the size of the bore or the cylinder throats, but one of the stamps on the barrel says .22 Magnum. Was the gun converted to one of the .22 centerfire standard production or wildcat rounds available in the '50s and '60s?
The barrel is probably not original to the gun, and the cylinder may be a replacement too, depending on whether bore diameter changed. Do you see the Vxxxx serial number on the flat underside of the barrel or the rear face of the cylinder? The original parts would have had those markings.
Interesting rear sight. Usually elevation and windage are both controlled by slotted screws. In this case, elevation could be adjusted by turning the knurled disk. I don't know who made that.
S&W won't touch a gun that old even if it has not been modified. I would encourage you not to try to refinish it, but just take care of it as it is and let it remain a family heirloom.
EDITED TO ADD: Boy, what a flurry of responses. Everybody piled on with pretty similar observations while I was writing up a few comments. And yes, welcome to the forum.