I think both P-H and Cogswell & Harrison made these.
I've posted before about reading an article in, "South African Panorama" back about 1980 about a fellow who lived in the bush and wore one of these .22 conversions. He mentioned the advantage of cheaper .22 ammo. Keep in mind that SA was under UN sanctions then, and ammo costs were probably pretty high for most calibers.
Yours are the best photos that I've seen of one of these guns, and I think most conversions were carried out on six-inch barrels.
People here keep asking, although the info is in most books on S&W and about military small arms of the era, but here goes again:
Prior to April, 1942, four, five, and six-inch barrels were furnished to the Commonwealth on K-200 revolvers. After that date, only dull finished (looks like Parkerizing but called Midnight Black) finishes and smooth stocks were sent. Earlier finishes were blue, then sort of brushed blue. I've never seen one of those brushed transition guns. I suspect they're the rarest of the .38-200 ones.
In all, over 568,000 British Victory Models were sent, and many were defaced by surplus dealers after the war. Barrels were cut down, sometimes eliminating the front lock, and some were made into .22's. I think the .22 conversions were among the nicer modifications. I don't know how well they work, but Parker-Hale was a staple of the UK gun trade, and their military conversions of .303 rifles were also popular. Their gun cleaning supplies were the standard over there and throughout the former Empire.
Gun author Geoffrey Boothroyd mentioned that due to currency restrictions in the 1950's, new US guns were rare in Britain. He made up a fast draw Victory Model with some Askins-like mods and that gun appeared on the hardcover edition of his friend Ian Fleming's James Bond book, "From Russia, With Love." I would appreciate it if one of the more computer savvy members will find that book in a Search and post links here. I guess we can't post the photo for copyright reasons.
Due to the money/import restrictions, Fleming couldn't find a new Centennial and he wanted one after Boothroyd convinced him that Bond should have one. He had to get his on a visit to New York, of all places! You can see pics of him with it on the back cover of some of hs paperbacks, in the old editions. (Others had him holding a Colt Official Police .38 given to him by the head of the OSS. His actual carry gun while a Naval Intelligence operator was a Browning Baby .25.)
This may be more than you want to know, but the mods to the postwar surplus .38-200's were many and varied. Most were unfortunate.
Frankly, I think your converted .22 is a collector's item, but you can learn more on Gunboards in the British Gun Pub forum there. It should interest not just S&W colletors, but those who collect British arms.
I earnestly entreat you to find a copy of Geoff Boothroyd's book, "The Handgun." It is quite probably the finest single volume ever on its subject, and has been reprinted several times since its appearance in the 1960's. I think it turns up on sites like Amazon.com You can often get one pretty cheaply, as it's never had the legions of fans here after it like original copies of Keith's books. Boothroyd was little known in the USA, but was one of the most knowledgeable gun writers of all time. His expertise spanned the whole range of handguns, from matchlock to modern wondernines. That book is copiously illustrated, and is a fine item to have. Skip a movie or something and locate and buy a copy. It'll save you asking a lot of questions here.