At a glance, Pelagius doesn't seem to have been spouting off anything too strange. Anti-predestination, pro-salvation through works. Why were so many in the church threatened by this?
Additionally, how strong did Pelagianism become in Britain, and did it ever have much hold beyond the island?
[Late Antiquity] - [UK] - [Religion]
Pelagius was, as it sounds like you realise, from Britain. But he didn't stay in Britain and Pelagianism is not associated with Britain nor did it have its stronghold there. Pelagius appears in Rome and teaches there for quite some time, but came (fled) to Carthage in 410 due to the sack of Rome, and then east to Jerusalem.
It was in Carthage that he came into fierce conflict with Augustine, bishop of Hippo.
In fundamentals, Pelagius' position on free will is that humanity is so constituted that they can choose to do what is right, and that the effect of sin is not to render it impossible for humans not to sin. 'Grace' in the Pelagian theology are the helps that God provides so that humans can live morally upright lives.
It is partly difficult to reconstruct accurately Pelagius' own beliefs and teachings because of the fact that they were eventually condemned, which led to them surviving primarily in quotations from his opponents.
Opposition to Pelagius centred on the way his understanding of free will, grace, and the effect of sin undermined (according to his opponents, of course) fundamental positions of Christian teaching. Augustine, as one of Pelagius' main opponents, viewed the effect of the Fall, and sin, as being so detrimental to the human condition that it is not possible not to sin (non possum non peccare, as he says), so that the remedy of grace in the Christian life must be more than just 'good example', and effect a change in the nature of the person. This he tied to baptism, and hence the strong emphasis on infant baptism as a means of grace that developed in the Western tradition.
As with all controversies, there were mixed reactions on either side. Many were impressed by the moral rigour of Pelagius and his followers and associates. Likewise, many felt that Augustine's 'pessimism' about the human condition went too far. Nonetheless, both on a theological and political level Pelagius and his theology 'lost'. Pelagius was condemned and his theology declared heretical. In the views of those who 'won', it undermined fundamental beliefs of Christianity related to human nature, evil, grace, and how salvation worked.
Aside from the "theological" nuances of the debate, it's also worth considering the political context. A backwoods ascetic shows up in Rome and is horrified at the behavior of Christians (among whom were many aristocrats and other elites who had become Christian through marriage or by convenience). This is a time when it was not unheard of to avoid baptism until your deathbed, on the belief it would absolve you of all your sins. Pelagius basically calls this attitude BS and challenges what he considers the moral depravity of the elite. You can do better, Pelagius asserts. You have power of your choices. This could be seen as a threat to many powerful people in Rome, obviously. Augustine thinks this view of the will is naive and unscriptural, of course, and develops his alternative theory against Pelagius. But hermeneutics and theology aside, it's not hard to see why Augustine's account might be easier for powerful Christians to swallow. To this day, many "left-wing" Christians are called Pelagian for what others regard as their utopian moralism. If you're trying to be a ruler or elite, you don't want to be held to some ascetic ideal for your personal conduct.
Richard Fitch, "The Pelagian Mentality: Radical Political Thought in Fifth Century Christianity," in Alexandre J.M.E. Christoyannopoulos ed. 'Religious Anarchism: New Perspectives' (Cambridge Scholars Publishing, 2009) pp. 2-29.