Born into a family of artists in London, England, his early career was as a book illustrator, for example in Hans Christian Andersen's Tales; The Arabian Nights, (1899); Tales From Shakespeare (1902), and Twelfth Night (1908), Charles Kingsley's The Water Babies (1915), and Walter de la Mare's Peacock Pie (1916).
In the course of this however, he wrote and illustrated two children's; books, The Adventures of Uncle Lubin (1902), and Bill the Minder (1912); these are regarded as the start of his career in the depiction of unlikely machines. During World War I he drew large numbers of cartoons, collected as Some "Frightful" War Pictures (1915), Hunlikely! (1916) and Flypapers (1919), depicting ever more unlikely secret weapons being used by the combatants.
Besides these, he produced a steady stream of humorous drawings, for magazines and advertisements. In 1934, he published a collection of his favourites as Absurdities, featuring such subjects as "The Wart Chair. A simple apparatus for removing a wart from the top of the head", "Resuscitating stale railway scones for redistribution at the station buffets", and "The multimovement Tabby Silencer" (this last for automatically throwing water at serenading cats); Most of his cartoons have since been reprinted many times in multiple collections.
The machines he drew were usually kept running by balding, bespectacled men in overalls. The machines were frequently powered by steam boilers or kettles, heated by candles or a spirit lamp; often there would be complex pulley arrangements, threaded by lengths of knotted string. Robinson's cartoons were so popular, that even to this day in Britain, the name "Heath Robinson" is applied as a shorthand for an improbable, rickety machine barely kept going by incessant tinkering. (The corresponding term in the US is "Rube Goldberg", after an American cartoonist with a similar style in machinery.)