Gay subtext?
Gielgud had been outed in 1953 by his arrest in a public restroom. While not openly gay, Dirk Bogarde had played gay men in the 1961 film "Victim" and "The Servant" two years later, which in those days was pretty daring, especially for a matinee idol, which may have aroused contemporary suspicions.
Moreover, Bogarde's Sebastian is being spied on by his employers, as if he had a secret.
I'm not sure how significant all that is (a lot of gay actors played straight roles).