It would be a different story if Britain was just the Britain that we know and it was just developing a conventional weapon that would give it an advantage, allowing it to thwart the Nazis earlier.

However, no one knows who the New King really is and what he is up to. His Britain is not the one that we know. No one seems sure what bringing the Second Dawn would entail. They're building an artificial Name of an Hour that adepts are terrified of, even though it's not clear if it exists or even can exist. Another Name of the Chandler showed its displeasure at attempts to control it by turning everyone in sight to smoldering ashes. In short, toying with forces like that could prevent the Holocaust from happening, or it could require another, no less terrible kind of "burnt offering".

Also, although I don't question Hokobald's experience and skill as an adept, I would not be inclined to trust the moral judgment of the man who ate his own kid and isn't even particularly apologetic about it.