Dirk Bogarde was cast at the 11th hour. Bogarde originally turned down the film and Tom Courtenay was cast then Bogarde changed his mind due to financial reasons. Courtenay ended up starring in another spy comedy called Otley.
This movie was made and released about four years after its source novel 'Night of Wenceslas' by Lionel Davidson was first published in 1960. The book was his debut novel and won two awards, the Author's Club First Novel Award and the Gold Dagger Award of the Crime Writers' Association.
The code number of Nicholas Whistler (Dirk Bogarde) was 008. The film's American titles 'Agent 8¾' / 'Agent 008¾' vary this. These titles spoof James Bond's code number of 007. This film's storyline actually has an Agent 007 who is killed off at the start of the movie.
The meaning and relevance of this film's 'Hot Enough for June' English release title is that it refers to the name of a code used to identify Whistler (Dirk Bogarde)'s contact in Czechoslovakia.