The introduction of rabbits to England post-dates the Norman conquest.
We know people are them because when the Romans left ("dark ages") they were eaten to extinction:
"Butchered hare and chicken bones appear in the archaeological record hundreds of years later, among Roman-period food waste. At this time, Sykes said, hares were farmed for food, and the Romans introduced rabbits to the island, although hares and chickens continued to hold religious associations for Britons. After the Romans withdrew from Britain in A.D. 410, the populations of hares and chickens crashed, Sykes said, and rabbits went extinct."
Source: https://archaeology.org/news/2020/04/10/200413-britain-hares...
So what is going on in medieval times, centuries later, is they are being re introduced and horded by the Anglonorman aristocracy. This could simply be because, of course, half of England then is in today's France. The Plantagenet dynasty is even more French than the earlier Normans, who are of course mostly ex-Vikings. Later, at peak, the "English" Angevin dynasty territories stretch south from say Calais all the way thru Occ country to the Basques; and are intermarried with Spain and France. There's rabbits everywhere, trivial to bring back to Britain.
But they were apparently difficult and expensive to farm (which seems crazy as they breed like... rabbits) but this is perhaps explained by climate change-- the medieval warm period was about 950-1250 and then it began to get much colder. For example by 1315-1317 there was horrific famine caused by crop failures and abnormal cold summers. In this context the rich people are laboriously farming rabbits in artificial warrens inside of managed game preserves and poor hungry people get executed all the time for eating.
A good book for this era is Tuchman's 'Distant Mirror' which is like Game Of Thrones meets zombie apocalypse. Don't read it if you're French. It may be the reputational nadir of French civilization?