The actor died in hospital at the age of 89 after a recent fall from his mobility scooter.
Maynard, real name Walter Williams, was best known for playing Claude Jeremiah Greengrass for ten seasons of the long-running TV series.
He also starred in five Carry On films and 1980s TV shows The Gaffer and Minder.
Maynard initially retired from acting in 2000 after suffering a number of strokes, but then returned to his role in Heartbeat spin-off The Royal in 2003.
His daughter-in-law, actress Jacqueline Reddin, said: "He was larger than life and he just loved showbiz.
"He was so proud of the fact that he had been working for 81 years."
(c) Sky News 2018