So, when did the English Civil War start?
A straightfoward question that actually can't be answered without raising some more questions. Which war are we talking about? There were actually several, all during the same period, all over what now makes up the UK. We can have the English Civil War, the English Civil Wars, the British Civil Wars and the Wars of the Three Kingdoms.
In the interest of putting all the cards on the table, lets look at the Wars of the Three Kingdoms, the broadest term.
In 1639, the first of the Bishops' Wars took place in Scotland. After ascending the throne in 1625, Charles I followed up on the plans of his father, James I, to centralise the Scottish Church. Unfortunately for Charles, most of his views were seen by the very Protestant church as essentially Catholic and they refused to follow his guidelines. Charles' 'New Book of Common Prayer' in 1637 was especially contentious, so much so that, in 1638, most of Scottish society signed a National Covenant pledging disobedience to the prayer book and any other 'religious innovations' that Charles might come up with.
So, in 1639, Charles did what all despots with a belief in Divine Right eventually do, and started a small civil war to show his authority, and enforce the Prayer Book through arms. He organised 20,000 men and an overly ambitious, overly complex plan to occupy Scotland. This was quickly stalled by Scottish Covenanters occupying key towns in advance, essentially thumbing the nose at Charles' plan to invade across from Ireland. Charles eventually arrived with an army and said that he wouldn't invade Scotland if the Covenanter Army stayed north of the border. The Pacification of Berwick was signed, a peace treaty between the two sides.
This lasted a whole year! In 1640, Charles, desperate to get money to re-wage war with the Scots, had to recall Parliament to try and get some taxes out of them. Whilst the Scottish Parliament was razing Royalist holdouts in Scotland, Charles scraped together enough to raise an army. The Scottish Army, led by Alexander Leslie (a 30 Years War vet) pushed their way across the River Tyne and invaded England, taking Newcastle. Lord Conway, the British commander, had withdrawn to Durham, his army a rioting, routing mess. Parliament, who agreed that many of Charles' plans were verging dangerously close to Catholicism, refused to pay for his army anymore. Once again, Charles was forced to make peace. That was two for two for the Scottish Covenanters.
Things were quiet for Charlies, for a couple of months. He looked to Catholic Ireland to raise an army that could put down the riotous Scots. This proved to Scotland and Parliament that Charles was a tyrant who would impose his will on the masses and there was talk about sending an English army to Ireland to pre-emptively put the Catholics down. This followed years of Catholic oppression under Wentworth, Lord Deputy of Ireland (who's depredations were so bad that the first thing Parliament did when returning was try him and execute him - and they also hated Catholics!). Fearing an imminent invasion, in 1641 a cadre of Irish Catholic gentry led a rebellion that overthrew English Protestant rule in a number of areas of the country. Response from Charles, and Parliament, was slow due to the political tensions. An army was sent over and fighting continued into 1642 where things ended in a stalemate due to...the first English Civil War! Eventually, those rebel Irish areas banded together and formed the Irish Confederacy, a Catholic ruling government that aligned with Charles during the Civil War.
Things weren't going particularly well for Charles, as we've seen. The important thing to remember about Charles I is that he was fully convinced of his Divine Right to rule. He believed that he was placed on Earth to convey God's will and rule the country based on that - therefore, it was blasphemy for him to be wrong, about anything, ever.
This is why he kept running into such issues with his Parliament. For a long time he had disbanded Parliament, refused to listen to the people and did not seek any guidance. When he had to recall Parliament (to get more money to fight the Scots) he was reminded that they disagreed with him on pretty much everything.
In January 1642, Charles attempted to arrest 5 MPs who were particularly opposed to him. They escaped down the Thames and Charles was, once again, shown to be pretty inept, even at tyranny. He fled London, handing Parliament the biggest spot for militias, weapons stores and trade. Parliament issued the Militia Ordnance, taking control of all the trained bands in the country. In August 1642, Charles raised his standard at Nottingham Castle, declaring war on Parliament and starting the first English Civil War. The Scottish Covenanters raised their army to join Parliament and the Irish Confederacy started sending troops across to support Charles.
The Scots had a particularly important role to play in the war. In 1646, Charles, having faced a series of defeats the previous year, fled from Oxford to Newark, surrendering to the Scottish commander of the army sieging the town. The Scots took off back to Scotland and Charles was imprisoned. By surrendering to the Scottish Covenanters, Charles was hoping to exploit growing divisions between the Covenant/Presbyterian faction (who agreed that Charles would remain king) and the New Model Army (who did not). When the Puritans failed to dissolve the New Model Army at the end of the war, the Scottish invaded and all of the Royalists who hadn't yet been killed or turned (particularly in Wales) rose up in rebellion - 1648, the Second English Civil War!
None of it went particularly well for Charles. The New Model Army was a force to be reckoned with, and Cromwell and Fairfax firmly pounded the poorly organised Royalist uprisings. Order had been essentially restored within the year. Charles was tried and beheaded in January 1649.
England became a Commonwealth, eventually under the guiding hand of Lord Protector Oliver Cromwell. Meanwhile, the Scottish crowned Charles II and an alliance was also made with the Irish Catholics. In 1649, Cromwell took the New Model Army into Ireland to suppress the Irish Confederacy. He stormed through the land, massacring the garrison and many civilians at the Siege of Drogheda and sacking Wexford during negotiations. In 1650, Cromwell left the army conquering Ireland to raise an army to invade Scotland, the third English Civil War. Whilst Cromwell was fighting the Battle of Dunbar, Charles II counter-marched into England. He marched hoping that he would pick up Royalist supporters on the way but Wales and the South refused to rise. In 1651, one year after Dunbar, the New Model Army fought the last dregs of the Royalist cause at the Battle of Worcester. Charles II was defeated and escaped to reign in exile.
The end result of the Wars of the Three Kingdoms was that the Royalist cause was dead and the Parliament Interregnum was instituted for the next 9 years, led primarily by Oliver Cromwell. On his death, the Lord Protectorship fell to his son, Richard and, after this proved to be a mistake, Charles II was invited back over to rule a much-reduced monarchy.
So, to come back to that original question - when did the English Civil War start? - I'll give you some answers:
a) In 1639, with the Bishops' Wars, due to Charles interfering with the Church.
b) In 1641, with the Irish Rebellion, due to Catholic oppression - this would continue until 1651 with the end of the Cromwellian conquest of Ireland.
c) In 1642, when Charles I raised his standard and declared war on Parliament, starting the first English Civil War.
d) In 1648, when Scotland invaded England to keep Charles I on the throne as king.
e) In 1650, when Scotland invaded England (whilst England was invading Scotland) to put Charles II on the throne as king.
Hopefully that's cleared things up for you!