The Wars of the Three Kingdoms between 1639 and 1653 included a lot of Anglican/Episcopalian vs Presbyterian Protestant fighting. In 1638 King Charles I tried to force the Church of Scotland (a Presbyterian church) to become more like the Anglican Church of England. The result was the Scots went to war against Charles and defeated him twice, in 1639 and 1640. This ensured that the Church of Scotland didn't become Episcopalian in nature. During the English Civil Wars which followed from this conflict the allied Scottish and English Presbyterian and Puritan Protestants often claimed Charles and his Anglican bishops were allied with Rome and Catholicism, and used this as propaganda to recruit more men. The Civil War period was itself for the most part a civil war between the various denominations of Protestant within the British Isles (though there were many factors aside from just religion). The later Jacobite rebellions such as those in 1715 and 1745 are often styled as conflicts between British Protestants and Catholics, but in reality as much as half of most Jacobite supporters were Episcopalian.

Sources - Antonia Fraser: Cromwell, Our Chief of Men. Diane Purkiss: The English Civil War, a People's History John Prebble: Culloden I have more if you want.