Disclaimer: I have not watched "The Tudors", so I can't directly comment on its accuracy. As for the progress of the English Reformation, things were... complicated. It would take a book far beyond the scope of a Reddit post to cover the events of the 16th century English church, which contained several dramatic switches between Protestant and Catholic under successive monarchs. But I'll focus on Henry VIII's time, since that's who you mention - broadly speaking, I would say in the beginning it was sudden and unexpected, yet also gradual. Henry's initial break with Rome famously happened for political/personal reasons rather than theological ones. Back in 1521, the pope gave Henry the title "Defender of the Faith" for writing a treatise against the doctrines of Martin Luther (Henry probably had help from theological advisors, but odds are it wasn't entirely ghostwritten and Henry did contribute in some way). In that sense it was sudden, how in such a short period of time he went from a defender of the pope to declaring his independence.

Yet Henry remained theologically much more Catholic than Protestant for his entire life, in fact making it illegal to publicly profess certain Protestant ideas like denying transubstantiation. His rupture with Rome was based on his desire for divorce, and the issue was not one of theology. The question was who was the earthly ruler over the institutions of the church; the Reformation of Luther and Calvin was much more about doctrine and practice. In that sense it was gradual: it was years after the separation with Rome that any measure of theological or practical change really took hold. There were dedicated Protestants in England from the 1520s on, but mainstream religious life remained quite Catholic as long as Henry reigned.

One particular event that bears mentioning as a sudden shift was the Dissolution of the Monasteries, which was a political and financial move on Henry's part, but had cataclysmic effects on England's religious life. In the wake of the separation with Rome, monastics (monks, nuns) were some of the most vocal critics and most outspoken about allegiance/obedience to the pope. The monasteries were also huge lamdowners and a powerful, popular presence in the country. Henry declared that the monasteries were to be dissolved, the religious orders dispersed, and their property confiscated - he silenced his critics, gained a huge amount of money, and surprisingly pulled it off with relatively little opposition. There were protests, but they were quelled with executing the ringleaders and making never-kept promises to the rest.

Tl;dr - it depends on what you mean; the theological changes were mostly gradual, but the structural changes were quite dramatic.