samantha:
You have a British Service revolver from 1940 or 1941.
In 1940 Great Britain and the British Commonwealth were at war with Germany, S&W supplied guns to the British under a direct contract and later through an inter-government agreement. The guns supplied via the US Govt under the Lend Lease agreement were marked United States Property.
BSRs were in .38 S&W caliber and usually had a five inch barrel. Other than that they were mechanically identical to the .38 S&W Special Model of 1905 4th Change which was a common police revolver.
The barrel is measured from the frame in front of the cylinder to the muzzle, I think you will find yours is a 5 inch gun.
767" and 3 1/2 tons are British proof marks, .767 inches is the length of the .38 S&W case, 3.5 tonnes is the pressure of the 'proof load' fired to ensure the gun would not blow up when fired.
A lot of these guns were reimported after the war and sold as surplus. Often the chambers were bored out so the more common .38 Special cartridge would fit. If a .38 Special cartridge will fit then you have a converted gun, don't fire anything other than standard pressure lead loads in a converted gun as the cartridge is not a tight fit to the chambers and increased pressure loads could result in split cases and gas escaping.
If the .38 Special won't fit then the gun is still in its original caliber. .38 S&W ammo is rare and relatively expensive but still available.
36788 is an assembly number, used to track parts in the factory. It has no meaning after the gun is completed. S&W did not introduce model numbers until 1957.
895197 is the serial number, this is the only number recorded if sold through a gun dealer.
I'm not sure what the WB means, could be Britsh markings or could be a previous owners.
The screw in front of the trigger guard is correct for that model, up until the 1950s S&W used 5 screws in the frame, 4 in the side plate and and one in front of the frame. These are commonly known as 5 screw models.
The grips are not original, they are a fake stag horn that was commonly used to dress up the surplus guns sold in the 1950s.