I don't think the friendship was homosexual - I think the writer intended to bring the point into question.
I watched the movie thinking all was heterosexual until Henry's mom gave her little speech calling the friendship unnatural and Henry acted like he was having a heart attack after he sent his family out.
I don't believe there was anything more than friendship here, but I agree with your main point - the movie is implying there was something more going on, at least with Henry. For one thing Henry, more than once, bemoans the fact that Becket does not 'love' anyone - most notably after
Gwendolyn's suicide
. The king's family disapproves of his 'unnatural' attraction to Becket and get snarky about it more than once.
I'm American so I can't speak to this with a native's knowledge, but O'Toole's Henry is larger than life, and his loves and hates seem extreme. His emotions are larger than life, more dramatic than those of a commoner. I think it's fair to say over the top, but it was an over the top life. I can understand a king, who has a king's sense of himself, extending his emotions to a commoner and not having his affection - platonic or otherwise - returned would get a little obsessed about it.
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Good point. King's thought they were divinely appointed so they would expect to have what they want. Partly also, there is generally a battle of wills - church vs state, which came to a head during Henry VIII.
I don’t think there was any suggestion their relationship was sexual, though I thought it was odd that the movie began with Becket in the bedroom of the woman Henry was bedding. I guess he was keeping watch.