For some background, the Pope in question was Clement VII (Giulio di Giuliano de' Medici). Like other Medici, Clement was deeply involved in Italian politics. Upon his succession he also became deeply involved in continental politics. Without going too deeply into the Italian wars, Clement vacillated between Francis I of France and Emperor Charles V. Ultimately he chose poorly, Charles sacked Rome in 1527, and Clement was taken prisoner. Things didn't really improve in 1530 and the Peace of Barcelona. The Pope was firmly under Charles' thumb and had little room for maneuver.

By the time William Knight arrived in Rome 1527 (to ask for an annulment), the city was already taken and the Pope was already a prisoner. After that point it was extraordinarily unlikely that Clement would be free or willing to act for Henry and against Charles (and Charles' aunt, Catherine). The question of the English marriage was now firmly part of the greater competition between Francis and Charles. And in this matter Charles had a strong opinion and held all the cards.

So with background out of the way... Henry wasn't asking for a divorce. He wanted an annulment. Catherine had been previously married to Henry's brother Arthur. In order to marry Catherine in the first place, Henry had to get a special dispensation from Pope Julius II. In 1509 the papacy ruled that Catherine's marriage to Arthur wasn't valid, because it wasn't consummated. A ruling that, at the time, Henry was quite happy with. Now 18 years later, Henry was basically making an appeal that both he and Pope Julius II had been wrong and that Arthur's marriage was valid... meaning that Henry's couldn't be.

Even without Charles' influence, that was going to be an uphill battle. Catholic marriages were supposed to be indissoluble. Henry's already had a specific Papal dispensation, in order to get the marriage in the first place. To ask a pope to override a previous pope's ruling was going to be hard to achieve regardless. With Charles acting functionally as Clement's master, divorcing Charles' aunt was a complete non-starter. I don't think there's any evidence that Charles explicitly told Clement how to rule. But he hardly would have needed to. Canon law and political expediency were both very clear in this instance.