Well, as you know, William the Conquerer came in 1066. But before he came England was actually one of the most sophisticated and centralized monarchies in Western Europe as far as taxes went. It was the Anglo-Saxons who split up the country into Shires run by Sheriffs. And they had a land tax, the geld, that was collected annually. The rate of the tax depended on the needs of the monarchy (i.e. war v. peace). They were so sophisticated because of the Viking raids. The collection for the geld was originally to pay the Vikings to leave but as Viking raids decreased and the Anglo-Saxons grew stronger it became a simple land tax.

The Normans really adopted a lot of the preexisting government (although often put new people in place) since it was vastly more sophisticated than Normandy at that point. William created the doomsday book, the very large book of landholdings in England, which many believe was to facilitate tax collection. For the most part, the Normans kept this up. With Henry I adding the Exchequer, which collected revenue.

Their land tax system was not really that different than ours. Your value was assessed and you were expected to pay it to collectors from the Exchequer who gave it to the Treasury.

The King had many other sources of income. There were many different legal fines (the English loved to sue each other early and often, another thing that was different from much of Western Europe). They had revenues from their own vast land holdings. They would also fine the hell out of Jewish people until they were expelled from England.

Things got complicated after Henry II died. First, Richard I went on crusade, which required raising taxes. Then Richard I was kidnapped and ransomed, which required raising taxes. Also, under John and Henry III they basically lost almost all of their land in France, which meant the English throne no longer had those places as sources for revenue. And John, his successor, was horrible with money. Obviously he began to raise taxes and his barons revolted forcing him to sign the Magna Carta, which you know. This was about a lot of things but it was primarily about their insistence that they have the right to advise the King on all matters but primarily how the Kingdom's money was spent. Under the Magna Carta, he had no right to levy or collect taxes without consent of the Barons (interestingly this provision was actually repealed but it became custom anyway).

From this period on, there really is a lot of back and forth between the nobles and the monarchy. They were quiet during the reigns of good kings but quick to speak up and intervene in the bad ones. When that happened his only leverage was if he could out fight them. And he, sometimes, could not (Edward II, Richard II, Henry VI).

Henry III was horrible about wasting money. And that is when the nobles really began insisting that regular parliaments be held and that the king could not levy taxes without the consent of a parliament. Under Edward I, Parliament became an official thing vaguely resembling what we think of where the Lords, knights and burghers of the country would come when the King called. Although these people weren't really elected.

It got very, very rowdy. Parliaments became, essentially, a way to force the King to do the things you wanted him to do or else you wouldn't give him the money he needed. Some monarchs were great at dealing with them others were not. (Elizabeth I was famously great at tickling their balls and then giving them nothing they actually wanted from her see: the Golden Speech.) In addition to nobles using the parliament to get what they want out of the King or no taxes they often had their own problems with each other, which meant faction fighting in Parliament.

All Kings hated it and England was pretty jealous of the France that began to develop with its strong central monarchy, which had no such system and just taxed the hell out of their people as needed (Spoiler Alert: that eventually ends poorly). But the custom was never really challenged by the monarchy and it became consistent that you needed a Parliament to levy taxes. Even Charles I (way out of your timeline) who ruled without a Parliament didn't try to levy new taxes without it. But there was a high level of deference that was supposed to go to the King.

But, as I said above, taxation was not the King's only source of income. They had their own lands, they had certain fines and fees that they collected, there were certain feudal dues owed them by right. So, if the land was at peace it could be possible to rule without having to call Parliaments very often and just live within your means. The state didn't have the sort of obligations to people that modern governments have. But, even in peacetime, try asking a King to just live within his means and see how he responds.

The leverage of the King was obviously that he was the King and (hopefully) descended from a royal line, which was respected. Theoretically, he also had more vassals at his command to come to battle if need be and then, later, had a standing army. And people really did prefer a peaceful kingdom. It is usually easier to just pay your taxes than to march off to battle to square off against the king and force him to stop wasting your money invading Sicily.

The leverage of the Nobles was that if they could agree they could outnumber the King. Every Great House had their own vassals and basically their own armies (retainers) until Henry VII, wisely, abolished the practice. And that, really, the King had a hell of a time taking money from you if you wouldn't give it up.