Reddit mentions of Edward II (English Monarchs)

I cannot detail every medieval king of England - that would be too long. I can, however, outline very briefly the fates of 2 or 3 consecutive kings which might help explain that there was no hard and fast rule about counsel power vs. sovereign power:

Edward I is an excellent example of a king exercising sovereign power and effectively binding his nobility to himself and his causes. He was very active in creating policy, expanding the judicial systems, waging war in Wales, Scotland and the mainland. He worked extremely hard to be successful, and to make his kingdom successful. He was forceful enough that his nobles went along with his schemes, and Edward was always in charge. He was an excellent commander and strategist.

Now, contrast that with the fate of his son, Edward II. He was okay as a commander, but he clearly preferred not to fight. He was less interested in the exercise of power as a way of responsibly raising the success and prestige of the kingdom than he was in exercising power to benefit himself and, especially, his friends. His friends often had nearly as much power as he did, and they all - including the king - abused it to enrich themselves, thwart justice, and generally lord it over everyone else. So he had a council, but unlike his father's council which helped develop and implement policy, Edward II's council found itself struggling to get anything done because the favourites (Gaveston and later the Despencers) were running the show with Ed's blessing.

So what could the other nobles do? They tried a few things - they got parliament to back them in forcing Edward to get rid of his favourite, and to let them run the country in a more responsible manner. But then they fought amongst themselves and Ed was able to take the reigns back and recall his favourites. Eventually he alienated everyone, and his wife and son ended up rebelling against him (I'm being very general here) and eventually Ed was relieved of his crown, and either died/was murdered or hung out in Italy as a pilgrim for many years.

So, in short, it depended on the King himself. Henry VIII is another example - he was quite forceful after Wolsey's supremacy was over, but, as Robert Hutchinson has suggested in The Last Days of Henry VIII, some crucial decisions and documents may have been authored and signed by his intimates using a dry stamp because Henry was so ill. If the king was effective, he led the way. If he was egregious, it often caught up with him.

Also see King John I, Richard II, Henry III, Henry VI and James II of England. Other European countries are beyond my knowledgable purview.