Martin J. Asbury was born in 1939 in Uxbridge, Middlesex, was educated at Merchant Taylors School and at St. Martin's School of Art, London, and started work in strip cartoons, including assisting Dan Barry on Flash Gordon in Austria. After a period designing greetings cards, he got work at DC Thomson, drawing "Secret of the Sheridan Sisters" for Bunty and "Soldiers of the Jet Age" and "The Crimson Claw" for Hotspur, before moving to TV Century 21, drawing "Joe 90" and the football strip "Forward from the Back-Streets", starting in 1969. He then drew "Captain Scarlet" for Countdown, starting in 1971. When Countdown was relaunched as TV Action in 1973, Asbury got an early opportunity to work in colour on "Cannon". From there he moved to Look-In, where he drew more strips based on TV shows, including popular runs on "Kung Fu" and "The Six Million Dollar Man", written by Angus Allan, until 1981. He also drew "Doctor Who" for TV Comic in 1975, and a Star Wars strip for the TV Times in 1982.
He took over as artist on the Daily Mirror's long-running science fiction strip Garth following Frank Bellamy's death in 1976, and drew it until it finished in 1997, writing some of the later stories as well. He also drew a biographical strip of Elvis Presley for the Mirror, and "Teach Yourself Tennis with Bjorn Borg" for the Daily Express. In 1984 he moved into movie storyboarding with Greystoke: The Legend of Tarzan, Lord of the Apes. Since then he has worked on numerous films, including several in the James Bond and Harry Potter series.