A wild boar was, according to Fitz Kreiner, a kind of pig. The Eighth Doctor described the English variety as "often jeopardised", suggesting that the English wild boar had been near extinction on several occasions.
However, the Doctor told Anji Kapoor that he was responsible for reintroducing the wild boar to England in about the year 1987. He claimed that it happened because of an incident with a farmer who worked the land next to his house in Kent. During unexpectedly rough weather, a tree broke open the cage holding the farmer's continental boars. They crossed into the Doctor's land. He then taught them to talk, and they presumably continued to breed as undomesticated boars.
Brewster, a talking boar from centuries later, overheard this story and considered it to be heresy. Like many of his generation, Brewster held that the re-population of the English boar in the 1980s was the result of divine intervention, not mortal meddling. (PROSE: Mad Dogs and Englishmen)