In the OTL Battle of Jutland, at one point the entire HSF had managed to engage an isolated portion of the GF: Beatty was pursuing Hipper's battlecruisers with his 6 BCs and 4 Queen Elizabeth fast battleships, and Hipper managed to lead him straight back to the main HSF force. Beatty had allowed his force to get strung out, with the BCs out of signal flag range with the QEs. Each half of Beatty's force managed to escape the trap and lead the HSF back to the main force of the GF, but without the Fleet Battleturn it was a near-run thing, especially for the QEs.
Suppose the weather had been a bit clearer that day, so the Germans could have used zeppelin scouts as planned. One of the zepplins may have been able to bring word of Beatty's approach to the main body of the HSF, which could have deployed to cross Beatty's T and bring all their guns to bear.
Problem is, even though this is the HSF's closest brush with defeating a significant chunk of the GF in detail, it's still not enough. Even if the HSF sunk every single one of Beatty's ships, they'd still be outnumbered 24:16 in BBs, not counting the four British BBs temporarily out of service during Jutland (three in refit, and one brand new BB still being worked up to combat readiness). The HSF would outnumber the GF 5:3 in BCs, but that's nowhere near enough to offset the difference in BBs.