King Henry VIII (played by Robert Shaw) stands in total contrast to Thomas More. He's the Darth Vader to More's Yoda. He's the Joker to More's Batman.
More is a man who honestly isn't power hungry—as evidenced by the fact that he's willing to give up all of his earthly power and…well, die. Henry VIII, however, is intoxicated with power—he is followed by a band of yes-men, who constantly gauge his reactions, laughing hollowly when he laughs and remaining quiet when he's angry.
We see the King jump off his barge on the Thames, landing on his feet in the mud. His reaction looks uncertain, and his courtiers all watch with apprehension, guffawing when he finally decides to laugh. We feel like Henry is intentionally keeping them on their toes, toying with them. Also, he's sensitive about his intellect and is worried people don't think he's a smart enough king—despite the fact that he's so powerful, he remains insecure and touchy.
Essentially, Henry believes that he's committed a grave sin—he's married his brother's wife after his brother's death, and thinks that this constitutes incest. (Yeah, that would make us totally uncertain, too.) The Vatican gave him a special dispensation to do this, but he's come to believe that the Church was wrong.
When paying a visit to More, he says:
HENRY: Does a man need a pope to tell him where he's sinned? It was a sin. God's punished me. I've no son. Son after son she's borne me. All dead at birth, or dead within the month. I never saw the hand of God so clear in anything. It's my bounden duty to put away the Queen. And all the popes, back to Peter, shall not come between me and my duty! How is it that you cannot see? Everyone else does.
He cites chapter and verse from Leviticus to back up his argument, while More points out that Deuteronomy says something different. The king is not swayed by More's argument, however, and ominously declares that people who say that his current marriage is legit are high traitors.
We get the impression that, though the king may be intoxicated with power, bossy, and kind of a jerk, he really does believe in what he's saying. He really thinks God wants him to get a divorce.
That's our main encounter with Henry (a.k.a. actor Robert Shaw, a.k.a. Quint from Jaws), though we also get a glimpse into his wedding to Anne Boleyn after he's divorced Catherine of Aragon. He gets excited when he thinks he sees More at the wedding—which would mean that More has finally approved of him—but it turns out it's someone else. The King is bummed.
Unfortunately, we don't get to see how Henry reacts to More's death—which would be interesting, given that he's really the man responsible for it, even if Cromwell is the one who leads the attack on More.
But by seeing the way the king treats Cardinal Wolsey, we get the impression that Henry doesn't mind being ruthless. Wolsey was faithful to the king, attempting to pressure the Pope in order to secure the king's divorce… but Henry charges him with treason as punishment for failing in his mission. So, we shouldn't be surprised if the king totally turned against More and didn't have one smidge of regret about putting him to death.