He played Dr. Watson in "The Adventures of Sherlock Holmes" for the initial series and then left the programme after receiving an invitation to join the Royal Shakespeare Company along with his wife, Anna. They both considered the joint work to be the best idea for their young son, Tom, who was around 3 years old at the time. He was thought by many to portray Dr. Watson with an excellent style. He was replaced by Edward Hardwicke, whom he had recommended as his successor. Burke had earlier experience with Holmes having played the villain in an adaptation of "The Adventure of the Beryl Coronet" for the 1965 BBC series starring Douglas Wilmer and Nigel Stock.