A lot of the following is derived from Kieran Hickey's Wolves in Ireland which is a short treatment of, well, wolves in Ireland, but also covers some of England, Scotland, and Wales.

The wolves in England and Wales were likely wiped out in the fourteenth century; there are reports of wolves attacking cattle in Lancashire in 1304-05. There are two dates for the last wolves killed in Scotland, 1684 and 1743, but Hickey believes the earlier date is more likely. In Ireland, the last confirmed dates are 1786, with some patchy evidence for the early 1800s. The latter date is the last confirmed date for collecting a bounty in County Carlow, but there were sightings that persisted afterwards, but they could have been dogs that went feral or wolf-dog hybrids.

Obviously, human predation and destruction of habitat were key in the extinction of wolves in the British Isles. In Ireland, there was a bounty placed on wolves from the seventeenth century onwards and built upon the preexisting hunting regulations for the eradication of wolves. Cromwell expanded this bounty in 1653 for each wolf head and provided snares and traps at public expense. This led to an increase in the already robust trade to England in wolf pelts during the Tudor and Stuart period for the lining of cloaks. Based upon the decline in bounties paid off and exports of pelts. Irish deforestation and this increased culling led the Irish wolf population to decline precipitously around 1700, from which the population never recovered.

The general attitude towards wolves and their extinction was that they were vermin that were inimical to the functioning of civilized society. Many of the English settlers of Ireland were aghast that the countryside had wolves roaming throughout it. For some in the English state, the presence of wolves was a signifier of Irish barbarism. For example, Cromwell in 1650 laid the increase in the population of wolves directly at the feet of papist misrule which his invasion had rectified (of course, the expansion of the Civil War to Ireland created a temporary opportunity for wolves to move into territory previously occupied by humans). Stories of the "last wolf" in Ireland entered into many parts of local folklore, but there was seldom any real regret in these accounts about the extinction of these creatures.

This is an interesting question, and unfortunately I have no specific information for you. I can recommend I.G. Simmons's An Environmental History of Great Britain: from 10,000 Years Ago to the Present. It's been a while since I read it, but if memory serves it deals with the subject. You might also try Keith Thomas, Man and the Natural World.

More generally, the extinction of predators like bears and wolves at those dates is absolutely linked to human activity. I have no idea if there were organized, country-wide hunts to exterminate these animals, but humans were in direct competition with those species for habitat. And, those dates are fairly significant. In the first case, England after the year 1000 became a major supplier of wool to Flanders, where it was worked up into cloth. This obviously required a great deal of sheep, and therefore a great deal of land. The need to convert forests to greater numbers of usable pastures and to protect their growing flocks from predators must have intensified the competition between humans, bears, and wolves.

This competition was even more intense by the 17th century, when the populations of Britain and Ireland were larger and their dominance of the landscape both more intensive--land was worked harder through multi-course cycles of cultivation and pasture, and in more specialized ways--and extensively--virtually every corner if the archipelago was owned by someone. The 17th and 18th centuries also witnessed the true commercialization of agriculture, and therefore land use. Medieval restrictions on the grain trade, especially, were either allowed to lapse or outright removed, providing incentives for farmers to produce as much as possible. This found expression in the enclosure movement of the 18th century, which was really symptomatic of an intensification of human uses of British and Irish landscapes. Given the substantial chunks of open lands--"wilderness" is a frieghted term, but perhaps useful in this situation--that wolves require to sustain their populations, it makes sense that they would go extinct about that time; there was simply very little wilderness left at that point.

All that said, it wouldn't surprise me a bit if wikipedia were wrong and wolves persisted much lated.