Mussolini’s Consolation (Churchill Quotes)

Is Wikipedia right that Churchill admired Italian dictator Benito Mussolini for having the “good sense to shoot his son-in-law”?
It’s a great crack, but it is not verified.
Churchill had called Mussolini every name in his book: ”whipped jackal”…”organ grinder’s monkey”…”absurd imposter.” In 1944, after Mussolini executed his son-in-law, former Italian foreign minister Count Galeazzo Ciano, Churchill said in a broadcast:
…the successful campaign in Sicily brought about the fall of Mussolini and the heartfelt repudiation by the Italian people of the Fascist creed. Mussolini indeed escaped, to eat the bread of affliction at Hitler’s table, to shoot his son-in-law, and help the Germans wreak vengeance upon the Italian masses whom he had professed to love…. (Churchill By Himself, 365)

The Churchill son-in-law in question was Vic Oliver, an Austrian-born music hall comedian who had married Sarah Churchill in 1936, and whom her father regarded “as common as dirt.”
Oliver had the infuriating habit of calling his father-in-law “Popsie,” and in other respects he was—well—just not Churchill’s type: “A horrible mouth: a foul Austro-Yankee drawl. I did not offer to shake hands….”
It is sometimes represented that Churchill said something like this to Oliver himself, when Vic asked “Popsie” which war leader he most admired. Churchill supposedly replies, “Mussolini, because he was able to murder his son-in-law.”
But the only credible reference to the remark is newspaper proprietor Cecil King, who doubted it was genuine. King’s memoir, With Malice Toward None, contains this diary note from 20 July 1944:
The story going round the House [of Commons] this week—obviously concocted by some wag—is of Duncan Sandys at Chequers with the Prime Minister. Churchill’s favourite theme is of the great burden resting on him and of the unfairness that any one man should have to bear so great a responsibility. He was groaning away on the usual lines, so Duncan Sandys, to cheer him (according to the story), pointed out that Hitler had an even greater burden to bear—so had Mussolini—because, after all, everything was going wrong for them. To which Churchill replied “Ah! but Mussolini has this consolation, that he could shoot his son-in-law!”
Clearly, King thought this was a concocted quote—and no other source I have plumbed among Churchill’s family or colleagues states that Churchill made any such expression. In 1945 Sarah and Vic divorced. Churchill had warmed a little toward Oliver by then and was distressed over the breakup.
Winston Churchill did have a memory for good cracks, and had obviously been thinking of “Mussolini’s Consolation” in his March 1944 broadcast. But nothing indicates that he made such a remark with respect to Vic Oliver. If anyone can track it reliably, I would be glad to stand corrected.
For trivia fans, Vic Oliver was actually the very first guest on the long-running BBC programme “Desert Island Discs” in 1942. See Alex Hudson, “The Castaway who annoyed Churchill,” BBC News Magazine, 26 January 2012.