Yes, it is a British Service Revolver, sent to the UK under the Lend/Lease Act.
For all intents and purposes, the .38 S&W is the .38/200 regardless of what bullet weight was used. The Brits called it the .380 Revolver cartridge.
With that serial number, it is a rather late BSR. It probably shipped late in the year 1944, possibly early in 1945. Charlie might be able to pin it down more closely.
One issue is that in January, 1945, S&W started shipping the modified version with the new sliding hammer block safety and the serial number would have started with SV. But I'm not aware of any of those that were BSRs. Moreover, shipments to England stopped at about the same time.