The belief that "Oliver Cromwell banned Christmas" seems to be an ineradicable part of our folk history, but it's not really true. For one thing, Old Ironsides didn't have much to do with it - and for another, it all depends what you mean by "banned."
Following victory in the first civil war, a Puritan-dominated parliament had many reasons for wanting to crack down on Christmas. There was the theological argument: there is no scriptural authority for Christmas, which was adopted by the early church purely for political reasons. Nobody knows when Jesus was born, said the Puritans, but it definitely wasn't December 25th, a date chosen to fit in with existing, pre-Christian festivals. In any case, nowhere in the Bible are the godly permitted, let alone commanded, to mark Christ's birth in any special manner. Christmas was at best pagan, and at worst Roman Catholic.
Perhaps more significantly, Christmas had for a long time been seen by middle-class people as a riotous period, characterised by disorder and indolence. The modern, domestic xmas, where people might still overeat and overdrink, but would do so by their own hearths in the company of their own families, was still far in the future.
The old Christmas - the traditional Christmas we might call it, if we were in a mood to bait contemporary reactionaries - was celebrated in the streets more than in the home. It was a public fiesta not a private one, and it consisted in great part of what we would now term anti-social behaviour: demanding-with-menaces, mass drunkenness, home invasions and plenty of bullying under the guise of "Lighten up, it's just a bit of fun." It's reasonable to suppose that as many people dreaded the festive season as longed for it.
Above all, Christmas was about excess. It was, as it always had been, a time to eat too much, drink too much, play games and gamble, abandon sexual inhibitions, be noisy and unruly, sing loud and laugh louder. The ancient idea of misrule - that at this season, masters become servants, wives dress as husbands, and boys give orders to men - was arguably a safety valve in feudal society. In the infancy of capitalism, it was potentially dangerous.
So ideology, and practical concerns about law and order, coincided, and between 1644 and 1659 a series of laws were passed increasingly restricting both secular and religious observances of December 25th. There is considerable evidence that leading Puritans, understanding the political risks, were not keen on taking the anti-Christmas process too far - but that they were forced into more extreme measures by public opinion and particularly by militants within their own movement.
(To get the Cromwell myth out of the way: in 1647, General Cromwell was still mostly concerned with military matters rather than political ones, and was some way from being a leader of the government. He wasn't even present at the crucial 1647 debate. His own views on Christmas are unrecorded; the fact that he did not mention the controversy in surviving writings or speeches suggests that it was not a topic of great importance to him.)
It became illegal to hold special services on the 25th, or to decorate churches with evergreens. Traditional dances and theatrical performances were banned. Parliament sat as normal, and closing places of work or business, or workers taking a day off, was not allowed. Riots against the new regulations, some very serious and even involving loss of life, took place in various parts of the country especially at Christmas 1647.
It must have been a rough time to own a shop or other small business. If you closed on December 25th, the anti-Christmas mob would accuse you of supporting the sacrilegious festival, and attack your premises. But if you stayed open, the pro-Christmas gang would see you as a toady of the regime, so you'd get it from them instead.
Today, most historians think that the "ban" was unenforceable, or at least patchily enforced, widely ignored by those who cared enough to do so, and was more than anything an example of what is nowadays called gesture politics.
Which side of the Christmas argument was progressive, and which reactionary? Or does such a question even make sense? One of the central texts of British historiography is Sellar and Yeatman's 1066 And All That, ostensibly a parodic comedy but deceptively full of piercing insights. Its famous description of the Roundheads as "Right but Repulsive" and the Cavaliers as "Wrong but Wromantic" has been, for generations, a definitively influential summary of Britain's civil wars.
The Puritan government which set out to reform Christmas did so as part of the historic move towards capitalism - and therefore, socialists argue, towards socialism. It was the old ways vs the new. Christmas was associated with rural life, Catholicism, feudalism, and monarchy; its enemies represented urban living, protestantism, the transition to capitalism, and parliament.
But what we can't know at this distance is how many ordinary people, who by class or by inclination sided with the revolution against reaction, also wanted, once a year, to have a proper blow-out and get thoroughly wobbly, and resented the authorities which tried to take that from them.
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Sources:
www.historytoday.com/archive/feature/christmas-under-puritans
www.cromwellmuseum.org/cromwell/did-oliver-cromwell-ban-christmas
Cromwell and his women by Julian Whitehead (Pen & Sword, 2019)
www.nam.ac.uk/explore/oliver-cromwell-lord-protector
The battle for Christmas by Stephen Nissenbaum (Vintage Books, 1996)