So I had originally typed a more detailed answer than this, but the Reddit app closed and I lost it, so hopefully this more succinct answer will be ok.

It’s difficult to point to an exact time to say the power had shifted from the monarchy to the parliament, as you’ve correctly identified there’s a lot of unwritten rules and procedures that make it difficult to be exact.

However, there’s a few moments you can point to where there’s a big shift. One would be the signing of the Magna Carta, which took power from the king and guaranteed rights for lords (barons). This however wasn’t really a shift towards parliamentary government as we understand it today.

The English civil war (1642-51) was exactly about this issue. It was fought by King Charles I, who was obviously pro monarchy, against parliament led by Oliver Cromwell. However, the result of this war was that Cromwell essentially took power as a military dictator, so despite it starting over an issue of parliamentary rights and powers, it didn’t really help answer the question, and when Cromwell died in ‘58 parliament was quick to invite Charles II back from exile.

Charles II for a large part of his reign respected and often deferred to parliament. However due to his brother and heir being catholic, and growing fears that Charles himself was pro catholic, a conflict between Charles and parliament began to grow again. Repeated attempts of parliament to pass a bill excluding his brother James from the throne led to Charles eventually dissolving parliament in 1681 and ruling alone until his death in 1685.

When he died, James II (and VII of Scotland) succeeded him. His Catholicism was quick to cause great issues between himself and the Church of England, which parliament largely supported. In 1688 William of Orange, who was married to James’ daughter Mary (who was Protestant) was invited by parliamentary schemers to England, and he sailed over with an army, leading to James II fleeing and parliament offering the crown to Mary (and eventually also William). This became known as the “glorious revolution”.

In the negotiations between William and Mary and parliament there were some very important concessions made by the crown to parliament. The wording (and in a lot of ways the mere existence) of the settlement made it clear that kings in England got their power and authority from the people (and implicitly the parliament), rather than through divine rights. The Declaration of Right disallowed the monarchy to raise an army without parliamentary consent, effectively largely transferring the “monopoly on violence” - that Max Weber was to define centuries later as the most important aspect of the state - towards parliament. And the new “coronation oath” that William and Mary had to make proclaimed that the monarch has duties to the people and parliament, and would govern according to statutes agreed upon by parliament.

These changes were probably the most drastic swing from monarchy to parliamentary power in Britain. After 1688 the monarch still held a lot of power, but officially a large transfer of power can be seen towards parliament. From this point there was a more gradual shift towards the (almost) ceremonial position of the crown that exists today.

Edit: there’s been some really good elaborations / additions in the comments, definitely worth reading these too for a fuller picture.