Henry VIII was primarily concerned about himself and producing an heir. He did what he did solely to remove the obstacles that he faced to achieve this goal. All his actions dealt with his marriages on a case-by-case basis, and did not establish some sort of divorce legal precedent.
His first wife wasn't giving him male children and she was approaching the end of her childbearing years, so he searched for an excuse to annul his marriage (on the basis it wasn't a valid marriage in the first place). Divorce was out of the question.
When the church administration in Rome didn't support him, he found excuses to break away and found his own church. In fact, the only real difference in the Anglican church in the early years was that Henry was the head of the church instead of the Pope. Anyone who didn't support this view was removed from the church or executed. Later on, the Anglican church evolved in a different direction under more Protestant-minded leaders.
Only two of Henry's marriages were annulled. The very first annulment happened after he had been married for many years and was legally the most questionable. However, he was the law at that point, so he made it happen. The second annulment was more of a typical annulment, and happened when he had only been married for a very short time (a couple months) and was apparently quite uninterested in his new wife.
His second and fifth wives were executed for adultery. The charges were entirely fabricated for Anne Boleyn, but they were probably actually true for Catherine Howard.
The third wife died of natural causes and the sixth wife was still alive and married when Henry died.
So while it may look like Henry made divorce OK for English kings, he technically did not divorce anyone. He either found excuses to have the marriages annulled or they were ended by the deaths of his wives.