McCullough first came to public notice in 1934 with Aces Made Easy — or Pons asinorum in a nutshell, which he wrote with illustrations by Fougasse. This was a humorous look at the game of contract bridge, which was then very fashionable in England. He followed this the following year with You Have Been Warned — A Complete Guide to the Road an equally humorous book with the same illustrator. This was written at a time when the introduction could say “According to statistics, there is in Great Britain one car to every 33 persons ...”, so somewhat dated now.

After the war, McCullough and Fougasse again collaborated on light-hearted pamphlets, but with the serious intent of promoting road safety, Fancy Meeting You and Many Happy Returns — and How to Enjoy them

The official name of The Brains Trust was initially Any Questions?. McCullough was the first chairman, or “question-master” as the role came to be called. He used the name The Brains Trust from the start of the show in January 1941, and this became its official name in September 1942. The role of question-master was later alternated with others, but McCullough remained a regular until the radio version closed in May 1949.

McCullough took a small role in the Flanagan and Allen film Dreaming in 1945.