Jennings served in the Royal Signals during the Second World War. In 1943 his piece "Moses was a Sanitary Officer" was published in Lilliput magazine. Freelance work for Punch and The Spectator soon followed. Leaving the army with the rank of Lieutenant, he briefly worked as a scriptwriter for the Central Office of Information and then spent two years as an advertising copywriter; throughout this period his freelance work continued to be published.
In 1949 he joined The Observer, contributing a fortnightly column entitled "Oddly Enough" until 1966. After leaving The Observer, he continued to write until his death, mainly seeing print in Punch, The Times and the Telegraph magazine.