TLDR: That would be the reign of Henry VII (1485-1509), first of the Tudor monarchs.

Now… This isn’t a black and white question. The independent military power of prominent English magnates didn’t disappear overnight. Like every plank of the English constitution, it was a process. Royal power and noble power rode a roller coaster throughout the medieval period. Under dynamic kings like Henry I, Henry II, Edward I, and Edward III, royal power held sway. Ineffectual kings like John, Henry III, and Edward II, failed to overawe their barons and were in turn dominated by them. Even after Henry VII, baronial power remained strong in many areas. But Henry drew a line in the sand and I’m going to make the case that his reign holds the core of an answer to your question. Centralization of political authority is a hallmark of early modernity and Henry VII was the first early modern king of England.

The 15th century was England’s apocalypse of baronial power. During the Wars of the Roses (1455 - 1485), individual barons with private military and political followings, called affinities, came repeatedly to blows, first over who should advise the king, then over who should be the king. The king was Henry VI, who came to the throne as an infant after the early death of his conquering father Henry V. The man Henry VI became was not his father, not his grandfather, not any of his ancestors… he was a child in the body of a man. Kind and gentle, inconsistent and weak, he inspired neither hatred nor respect. Three generations of multiple lines had descended from Edward III. In the power vacuum of Henry VI’s long minority and feckless majority, all this royal blood consolidated into private power centers. This is often called “bastard” feudalism, an unfortunate term as it was built around political / military followings rather than landed vassalage. The effect was a nation of private armies, some supporting the king, some his opponents. Monarchy became a tool of political faction, and in the process the whole notion of divine monarchy was thrown into question. For 30 years the crown was up for grabs. It went from Henry VI to Edward IV, back to Henry, back to Edward, then to Edward IV’s son Edward V, who was usurped and murdered by his uncle Richard III. This is what Henry Tudor was facing in 1485 after defeating Richard III at the battle of Bosworth.

Henry Tudor did not have a strong claim to the throne. On his mothers’s side he was a Beaufort. The Beauforts were descended from John of Gaunt, Duke of Lancaster, who was third son of Edward III and the great-grandfather of Henry VI. The Beaufort line had originally been illegitimate but was later legitimized by Richard II. Henry’s father had been a half-brother of Henry VI, via Queen Catherine of Valois’ second marriage to a Welshman named Owen Tudor. Despite close relation to the king, the Tudors before Henry had no royal English blood. It is testament to how much royal blood had been shed that Henry Tudor became the focus of opposition to Richard III. His challenge was to stop the cycle of violence and re-establish the prestige and power of the English crown. He’d spent his adult life as an exile on the continent and had never run anything more complex than his own household, but he turned out to be the right man for the job.

Before even facing Richard, Henry pledged to marry Elizabeth of York (daughter of Edward IV, sister of Edward V) and declared himself rightful king. The marriage would join Henry’s tenuous Lancastrian connections with Elizabeth’s solid Yorkist lineage. Most of Richard III’s military support was eradicated at Bosworth field and the surviving few were deemed traitors. Through parliament, Henry passed acts of attainder against his remaining active or potential Yorkist rivals, ruining them financially and absorbing more property into the royal demesne. He passed the 1487 “Act on Liveries” which outlawed personal military affinities, ending the practice of “bastard” feudalism. Henry used parliament effectively to get what he wanted, but he also expanded the tools of monarchy.

Under the Tudors, central government grew more complex and professional. Henry VII didn’t invent the administrative state but he grew it and fine-tuned it so that it operated more efficiently than ever before. He established a council of 30 advisors drawn largely from the gentry, favoring merit over lineage. This council met in a room known as Star Chamber (there were stars on the ceiling) and would evolve into both a legislative and judicial authority, allowing later Tudor and Stuart monarchs to pass and enforce laws without parliamentary involvement. This planted seeds of tyrannical government which would contribute to the outbreak of civil war 150 years later, but it allowed the Tudors to keep their nobility in check.

Still, Henry VII wasn’t in a position to operate without noble support, and powerful vassals continued to wield much influence. The Tudors always had to contend with threats from disgruntled barons, but the individual military power these men could exercise had been greatly reduced. Crown and Commons would go to war in the 17th century, but the days of medieval noble violence largely came to an end after the Wars of the Roses, hastened by Henry’s stern rule and expansion of royal power.

Sources:

Alison Weir - The Princes in the Tower

John Gillingham - The Wars of the Roses

Dan Jones - The Wars of the Roses