Although he enjoyed a short stint as a child actor, appearing as Tom Brill in the BBC mini-series The Canal Children in 1976, he made his mark as a children's magician, and won the Magic Circle's Young Magician of the Year prize in 1981. After appearing in a number of variety shows on television, he was invited to join the cast of London Weekend Television's Copy Cats, a showcase featuring impressionists such as Bobby Davro and Gary Wilmot, in 1985. A second series, without Wilmot, followed in 1986. O'Connor received a writing credit for each series. His own children's show, Andrew O'Connor's Joke Machine soon followed, in which he told jokes and performed magic tricks and invited children to do the same. In 1986, he began appearing in ITV's popular Saturday morning children's series, No. 73. But shortly afterwards, he switched to the BBC to launch another Saturday morning children's series, On the Waterfront, alongside fellow ex-No. 73 host Kate Copstick. In 1991, O'Connor became the second actor to play The Head in CITV's arts and crafts show Art Attack presented by Neil Buchanan. In 1988, O'Connor also appeared regularly in short comedy sketches co-written by himself for the Observation round in ITVgame showThe Krypton Factor. In the same year, he took over from Jeremy Beadle as the presenter of the daytime game show, Chain Letters. He returned to acting to play the role of the computer in early 1990s children's sci-fi show Kappatoo but it was his career as a quiz-show host that took off, and he subsequently presented the UK version of Talk About, moved to Saturday night prime time in 1991 with One to Win, and returned to daytime television with The Alphabet Game. He has produced comedy and magic-related TV shows, including Peep Show, and most of Derren Brown's programmes. In 1993 O'Connor presented The Big Breakfast for a week while Chris Evans was on holiday, but did not enjoy the experience of live television. He presented an ITV & Family Channel game show called Family Catchphrase, which was a spin-off from Catchphrase; there were 100 episodes from 1994. One episode featured a young Simon Amstell and another featured a guest appearance from the show's creator, Stephen Radosh. Also in 1994, O'Connor played the lead in the touring musical Me and My Girl. He established Objective Productions with Michael Vine, where O'Connor holds the position of Chair. The company website claims the company was founded in 1991 but a 2005 interview with O'Connor in The Independent lists 1996 as the year the company was formed. According to Companies House, Objective was incorporated on 9 April 1992. O'Connor is an advocate of public service broadcasting, and in particular Channel 4, to whom he attributes a large part of his success as a producer.
In 1993, O'Connor played the title role in the musical BILLY at the Edinburgh Festival. He then went on to play the lead role of Bill Snibson in Me and My Girl in 1994 and the title role in the revival of Barnum in 1995 and 1996. He has also directed in theatre with productions of 42nd Street, Anything Goes and The Nerd on tour and The Odd Couple in the West End. In 2015, O'Connor Directed Derren Brown: Miracle with Andy Nyman.