Smith's father Kenneth was born in Tow Law, County Durham, and worked at a coal mine in the Second World War looking after the pit ponies. After the war he moved to London, and married Smith's mother, whose parents owned a greengrocers store in Chiswick, West London. When the government legalised High Street betting, he turned the shop into the first betting shop in Chiswick
While at Oxford University he produced The Tempest, and this led to his joining the Royal Court Theatre production team in London, and then Bristol Old Vic. He was also associate director of Sheffield's Crucible Theatre for two years. Later, he directed a theatre production of "Not in Front of the Audience".
When Smith was at Oxford, he performed at the Edinburgh Fringe with the Oxford University Dramatic Society. One year they shared a venue with the Cambridge Footlights, directed by John Lloyd. Lloyd later got the opportunity to develop the idea that became the satirical BBC television series Not the Nine O'clock News. Lloyd rang Smith to ask if he wanted to do it, and Smith agreed for £100 an episode This was followed briefly by Smith and Goody (with Bob Goody) and then the comedy sketch series Alas Smith and Jones, co-starring Griff Rhys Jones, its title being a pun on the name of the American TV series Alias Smith and Jones. He also appeared in Muck and Brass, and guest starred on an episode of The Goodies.
In 1981, Smith and Griff Rhys Jones founded TalkBack Productions, a company that has produced many of the most significant British comedy shows of the past two decades, including Smack the Pony, Da Ali G Show, I'm Alan Partridge and Big Train. In 2000, they sold the company to Pearson for £62 million.
Smith co-wrote and took the lead role in the space comedy Morons from Outer Space but the film failed to make much impact. His next cinema effort was better received as director of The Tall Guy, giving Emma Thompson a major screen role. Perhaps his best-known motion picture in America is Brain Donors, the 1992 update of the comedy classic A Night at the Opera, starring Smith as a cheeky, opportunistic cab driver turned ballet promoter. Paramount Pictures considered this film the outstanding comedy of the year, but when the producers left Paramount for another studio, Paramount withdrew its support for the movie.
Smith and Jones were reunited in 2005 for a review/revival of their earlier TV series in "The Alas Smith And Jones Sketchbook". Smith joked that "Obviously, Griff's got more money than me so he came to work in a Rolls-Royce and I came on a bicycle. But it was great fun to do and we are firmly committed to doing something new together, because you don't chuck that sort of chemistry away. Of course, I'll have to pretend I like Restoration"
Smith returned to the theatre stage after some 20 years in August 2006, appearing at the Edinburgh Fringe festival in Irish journalist and author Mary Kenny's play about Churchill's encounter with the Irish nationalist leader Michael Collins in 1921, The play initially caused some controversy, with Smith proposing to flout the Scottish ban on smoking in public places, but the scene was quickly adapted after gaining the required amount of publicity. The play was directed by Brian Gilbert and produced by Daniel Jewel.
In Autumn 2006, Smith starred opposite Belinda Lang in a tour of a new comedy "An Hour and a Half Late" by French playwright Gérald Sibleyras, which was adapted by Smith. He will then direct a West End revival of "Charley's Aunt" starring Stephen Tompkinson. From October 2007, he will play the role of Wilbur Turnblad in the London production of Hairspray at the Shaftesbury Theatre.
Smith ended up seriously ill in hospital in 1999 after consuming more than 50 Nurofen tablets, the culmination of a growing addiction to the pills. He said at the time that the pressures of film work were a contributing factor, along with a desperate need to ease the pain caused by gout. Partly as a result, he agreed to sell Talkback, but Smith admitted to restlessness: "I said to my wife that I needed to do something to get me out of the house".