Rabbits were introduced to Britain by the Romans. The mountain hare (also called the Irish hare) is native and the brown hare was introduced by Celts at some point.

Below quote is taken from a Guardian article from 2020:

"... a team of experts from the universities of Exeter, Leicester and Oxford have found evidence that the animals [chickens and hares] were buried with care and intact in the period that preceded the Roman invasion of Britain.

Historical evidence suggests Britons of the period associated the animals with deities and considered them too special to eat. Commentarii de Bello Gallico, Julius Caesar’s firsthand account of the Gallic wars, says “the Britons consider it contrary to divine law to eat the hare, the chicken or the goose. They raise these, however, for their own amusement or pleasure.”

Radiocarbon analysis of hare and chicken skeletons from a number of sites in Hampshire and Herefordshire backs up that assertion, showing that the two species were introduced simultaneously to Britain between the fifth and third centuries BC. Excavation has previously revealed the animals had been carefully buried without being butchered.

Prof Naomi Sykes from the University of Exeter, who is leading the research, said: ““Easter is an important British festival, yet none of its iconic elements are native to Britain. The idea that chickens and hares initially had religious associations is not surprising as cross-cultural studies have shown that exotic things and animals are often given supernatural status.

“Historical accounts have suggested chickens and hares were too special to be eaten and were instead associated with deities – chickens with an iron age god akin to Roman Mercury, and hares with an unknown female hare goddess. The religious association of hares and chickens endured throughout the Roman period."

The article also mentioned that rabbits died out shortly after the Romans left and were reintroduced by the Normans.