Most Roundheads sought constitutional monarchy in place of the absolutist monarchy sought by Charles. However, at the end of the English Civil War in 1649, public antipathy towards the king was high enough to allow republican leaders such as Oliver Cromwell to abolish the monarchy completely and establish the Commonwealth of England.
The Roundhead commander-in-chief of the first Civil War, Thomas Fairfax, remained a supporter of constitutional monarchy, as did many other Roundhead leaders such as Edward Montagu, 2nd Earl of Manchester and Robert Devereux, 3rd Earl of Essex; however, this party was outmanoeuvred by the more politically-adept Cromwell and his radicals, who had the backing of the New Model Army and took advantage of Charles' perceived betrayal of England by allying with the Scottish against Parliament.
England's many Puritans and Presbyterians were almost invariably Roundhead supporters, as were many smaller religious groups such as the Independents. However many Roundheads were members of the Church of England, as were many Cavaliers.
Roundhead political factions included the proto-anarchist Diggers, the diverse group known as the Levellers and the apocalyptic Christian movement of the Fifth Monarchists.