If anything, with the HSF gone, and thus the bulk of British destroyers freed from fleet duties, I would expect an earlier shift to the convoy system.Only now most of the Grand Fleet's destroyers will be available for escort duty once the Admiralty gets it's act together and begins forming Atlantic convoys. The RN's mine layers will also be a lot more active near the German coast.
A Trafalgaresque victory at Jutland has probably no short term effects on the land war. But it will give the Royal Navy complete control on the seas at the same time it will greatly reduce the strain exerted upon it. This is no good news for the Germans since this means the British have more ressources to throw against the U-boats should they come out in force again (which they will, the Germans won't have the choice now); more ressources to send into the ongoing Channel campaign; and more ressources to help tighten the blockade.
I don't know if the turnip winter can get worse than what it historically was, but yeah if such a thing is possible I'd guess the destruction of the High Seas Fleet is a good start...