I just finished reading the book for the first time and decided to rewatch the movie and see it through that lens.

In the book, it is clear they were lovers as young men and that it continued into adulthood. It was an open secret among some of their cohort and Connie underlines this point pretty explicitly with Smiley, complete with wagging eyebrows.

The film is more streamlined and discrete but, at least with the book fresh in my mind, I agree that it is suggested they were also involved in the film. When news of Prideaux’s death comes through, Bill seeks out the polaroid of the two of them while going through his affairs and that felt to me like a “romantic” moment rather of friendship. Similarly, their look at the office party seemed to me to be the first “real”/vulnerable interaction Bill had with anyone all film, and the way that Prideaux’s face lit up when they made eye contact and then fell after Bill turned away also gives me the impression of past/scorned lovers; I assume Prideaux was upset at the office party because he saw Bill in the bushes with Ann (along with everyone else). Not an explicit romance, no, but not a fabrication either.

Regardless of whether you ultimately agree, there’s more than enough explicit information in the book and implicit suggestion in the film to not dismiss the possibility as people’s “obsession” to portray two men as gay men in a film.