You seem to forget the German Navy knew they sunk the Barham. If the British were motivated to keep it a secret for morale reasons, the Germans were motivated to brag for the same reason.
Churchill was right, it was utter tomfoolery. What can one do if Churchill couldn't. In Britain, the reasoned mind is up against a society that pays royal louts a fortune, champions homosexuals, lets in the Muslims and asks it citizens to learn dhimmitude, can't fix their teeth, ... I give up.
Very famously they did not know if they sunk the Barham or not.
The U-Boat that fired the torpedoes hightailed it out of there, knowing that they had hit some ship in the flotilla but not that they had completely destroyed its crown jewel.
The German navy did not begin to suspect that the Barham had been destroyed until a few months later when they realized that U-331's November 25th sighting was the last visual the Reichsmarine actually had of that warship.