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This was first revealed in a paper called "Our Bloody Ships or Our Bloody System" published about twenty years ago IIRC. Jellicoe seems to have made pretty good choices on the day, but Beatty needlessly exposed his less armoured battlecruisers by approaching far too close to the Germans and giving up his gun and fire control advantage.
We couldn't very well admit it was a cock-up so Jellicoe was made First Sea Lord and Beatty was made commander of the Grand Fleet as though it was all a glorious victory. Jellicoe immediately suppressed the report written by the 3rd Sea Lord Rear Admiral Turner which correctly identified the sloppy ammunition handling as the problem. And just to make sure, he sent Turner off to command the China Squadron next!