Alan Rickman began his career as a stand-up comic before transitioning to acting, where he landed his first film role in 1964's Dr. Terror's House of Horrors alongside Christopher Lee. Throughout the 1960s and 1970s, Sparrow appeared in various films and television shows, including the 1969 sex fantasy Zeta One, Young Sherlock Holmes, and the acclaimed 1988 film The Accidental Tourist starring William Hurt, Kathleen Turner, and Geena Davis.
In the 1990s, Sparrow's career experienced a resurgence, with notable roles in the 1991 film Robin Hood: Prince of Thieves as the blinded retainer Duncan, 1993's The Secret Garden as gruff gardener Ben Weatherstaff, and the 1995 American coming-of-age film Now and Then as tragic drifter 'Crazy Pete'. Additionally, he starred in Tony Harrison's film Prometheus in 1998.
Sparrow's television appearances were equally prolific, with regular roles in the soap opera Emmerdale Farm, playing two different characters, and the comedy Paris. He also made guest appearances on numerous shows, including Hugh and I, Adam Adamant Lives!, Randall and Hopkirk (Deceased),Z-Cars, All Creatures Great and Small, Alas Smith and Jones, Rumpole of the Bailey, Ernie in Birds Of A Feather, and The Bill.
One of his most notable guest appearances was in the 1989 episode Danger UXD of the sitcom Only Fools and Horses, which garnered 16.1 million viewers, as porn shop owner Dirty Barry. Sparrow also appeared in the sitcoms One Foot in the Grave (1990) and The Thin Blue Line (1995).
In his later years, Sparrow continued to act, with his last appearance being in 2000 in an episode of the BBC's medical drama series Doctors.