The Ipcress File (1965)
This Michael Caine vehicle may have been produced by the team behind the Bond films, but its hero Harry Palmer is the antithesis of Ian Fleming's suave super-spy. While Connery's Bond was scoffing at the "noise" of the Beatles, Caine's Palmer was wooing 60s dollybirds by driving them to his place in his Ford Zephyr and rustling up a meal.
Called in to investigate a scientist's disappearance, Palmer's investigation takes a turn for the psychedelic when he's subjected to brainwashing. How very 60s.