Although the plot of A Man for All Seasons revolves around King Henry VIII and his indecisive romantic habits, the dude only shows up for one scene. How rude.
Luckily, that scene gives us some royal insight into England's resident rollicking regent.
The King's visit to More's home is a part of a big publicity tour arranged by Oliver Cromwell. This is a classic example of political stagecraft, with the all-powerful leader putting on a cute little photo-op in which he pretends to be roughin' it like the rest of us. Just check out all the sweet irony dripping off Cromwell's description of the tour:
CROMWELL: [...] You may not know that the King himself will guide her down the river [...] He will have assistance, of course, but he himself will be her pilot. (1.406)
Or, more likely, the King will turn the ship's wheel a few times while the pilot grabs a snack. Shade aside, the point we're making is that this tour is clearly just a PR move meant to make the King seem more relatable in the middle the current political turmoil.
Henry's hypocritical nature is highlighted in his interaction with More. At first, he tries to appeal with friendship and logic, two things that More values very highly. As it becomes clear that More won't budge, however, Henry drops the friendly facade and gets down to business, saying that More should do what Henry wants because he's the King, full stop.
Henry also tries to frame his divorce in religious terms. This, obviously, is a load of nonsense—Henry wants to get a divorce primarily because he wants a male heir, which Catherine has failed to produce so far. This is perhaps a valid thought process for a king, but the fact that Henry tries obscure it reveals some internal contradiction in his character.
It's not until the end of the play that we understand the nature of the contradiction in Henry's character—it's guilt. Check out Cromwell's description of the King's mental state:
CROMWELL: [...] He must submit, the alternatives are bad. While More's alive the King's conscience breaks into fresh stinking flowers every time he gets from bed. (2.570)
That might explain while Henry is conspicuously absent from More's arrest and trial. He sincerely doesn't want to do any of this—he especially doesn't want to kill a man he considered a friend—but he's been bound by his own political fears, as well as by the manipulations of men like Cromwell. Far from being a rote villain, Henry VIII is depicted in a fashion that simultaneously sympathizes with his situation and condemns him for his twisted actions.