"late medieval and early modern" = some time between the Plague and the industrial revolution.

"modern" = after the industrial revolution, which implies broad availability of farmed meat, leading to a gradual decline of hunting.

Yes, predation is a major factor in rabbit population control. And I'm counting British people as formidable rabbit killers, so I think we're in agreement there.

We're more or less in agreement, sure - I'm certain that Australians and Britains were equally eager to eat rabbits (during those times when that was a thing), the substantive difference being very few people in a vast land (AU) versus a mass of people in a pocket square of an island group (UK).