Well, 1645 is the year when the King begins to lose the Civil War, and Parliament begins to win. It's also the point at which the Independents begin to rise as a faction within Parliament - radicals advocating free tolerance of different religious denominations and less deferential to either Parliament or the King.
In 1646 the Cavaliers lose the First Civil War, and attempts are made by Parliament to negotiate a peaceful settlement that restores the King to power in a constitutional state. In 1647-8 the King outraged many by escaping and waging a new war (the Second Civil War) which he promptly loses.
Having lost much goodwill Parliament's attitude hardens and there are views that Parliament should impose a settlement on the King - perhaps even depose or exile him (although some speculate this was to try to spook the King into a settlement). But the Parliamentary side becomes increasingly divided, from the old, conservative Presbyterians who hate religious toleration versus the radical Independents.
In December 1648 Cromwell ordered Pride's Purge, which forced out of the Commons those Members who were adamant for a deal with the King, allowing a majority to exist which supported putting the King on trial for his life (the impact of the Purge was exacerbated by the fact that many not officially 'purged' opted to stay away from Parliament). This reduced-in-size Commons was called the 'Rump' Parliament.
As you probably know, the King was tried by an illegal Court of Justice in January 1649, defended the Laws of England and the Rights of the Subject, was summarily found guilty and executed. Shortly after, the Rump declared the Commons to be sovereign, abolished the House of Lords and the monarchy, and declared a Commonwealth.
The Commonwealth, unlike the monarchy and unlike modern states, had no single Head of State and no executive separate from Parliament. A Council of State was formed that acted as a collective government but it was composed entirely of MPs.
1649-51 was the Third Civil War, when the Cromwellian Army crushed revolts in England, laid waste to Ireland, and subdued Scotland. In 1652 Scotland and Ireland were incorporated into the English Commonwealth.
In 1653, following years of division and strife, the Rump Parliament, which had sought to have a policy independent of the Army, was dissolved by Cromwell, and he established a (temporary) dictatorship. He then established the Nominated Assembly, a unelected legislature based on the millenial predictions of the Fifth Monarchists, which ended in farce a few months later.
In December 1653 the Army enacted the Instrument of Government, England's only ever written constitution, which created the Protectorate, with Oliver Cromwell as Lord Protector.
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