McGowan attended the Simon de Montfort Middle School in Evesham, where he took lead roles in school productions, and went on to Evesham High School. He graduated from the University of Leeds with a BA English degree in 1986. He then went to the Guildhall School of Music and Drama in London, graduating in 1989.

In 1998, McGowan provided all of the voice characterisation in the 1998 revival of James the Cat for Channel 5 and later in the 2000s, went onto provide guest voices for Yoko! Jakamoko! Toto! and Planet Sketch both for CITV (Yoko! Jakamoko! Toto! later went onto air on both the BBC and CBeebies in 2008).

In 2004 he launched ‘the BIG recycle’ national recycling campaign. In August 2006 he appeared on Steve Wright’s BBC Radio 2 show to appeal to listeners to be more energy aware. In June 2007 he appeared on the James Whale Show on Talksport to also talk this issue.

He made a return to dramatic acting in 2005, appearing in the BBC’s adaptation of Charles Dickens’s novel Bleak House. He also appeared at the Chichester Festival Theatre in two plays; the first was a new translation of Nikolai Gogol’s The Government Inspector by Alistair Beaton, the second was a new play called 5/11, which was produced to mark the 400 year anniversary of the Gunpowder Plot. In 2006 he starred in the detective series Mayo. He also presented an episode of Have I Got News for You on 20 October 2006. He joined the Royal Shakespeare Company for the Christmas 2006 season playing Mr Page in Merry Wives: the Musical (a version of The Merry Wives of Windsor) opposite Judi Dench, Simon Callow and Haydn Gwynne.

McGowan was born in Evesham, Worcestershire, to Marion and George McGowan. Although they knew that their father had been born in Calcutta, India, Alistair and his sister Kay were unaware that their father had an ethnically Anglo-Indian background until McGowan explored his ancestry on BBC One’s Who Do You Think You Are? programme in an episode broadcast on 26 October 2007, four years after his father’s death.

In 2007 McGowan starred as Orin Scrivello (and other, smaller characters) in the West End transfer of the Menier Chocolate Factory’s revival of Little Shop of Horrors, and filmed My Life in Ruins, an American comedy film set in the ruins of ancient Greece. In 2008 he made his directing debut at Guildhall School of Music and Drama with Noël Coward’s classic comedy Semi-Monde.

In January and February 2008 McGowan starred as the eponymous protagonist of The Mikado by Gilbert and Sullivan, in a revival by the Carl Rosa Opera Company. On 21 April 2008 he took over the role of Emcee in Cabaret at London’s Lyric Theatre. In July of that year he appeared in a revival of They’re Playing Our Song at the Menier Chocolate Factory.

In March 2009 McGowan starred as the Duke in the stage version of Shakespeare’s Measure for Measure.

In January 2009 it was announced that McGowan in partnership with three other Greenpeace activists, including actress Emma Thompson, had bought land near Sipson, Middlesex, a village under threat from the proposed third runway for Heathrow Airport. It is hoped that the area of ground, half the size of a football pitch, will prevent the government from carrying through its plan to expand Heathrow. The field, bought for an undisclosed sum from a local land owner, will be split into small squares and sold across the globe. When interviewed Mr McGowan said: “BAA were so confident of getting the Government’s go ahead, but we have cunningly bought the land they need to build their runway.”

In 2009 he attended the Bromley Environmental Awards and was the celebrity guest at Bromley Civic Centre where the awards were presented to various schools in the borough.

Alistair appeared as a host on one episode of the fifth series of Live at the Apollo, which aired on 1 January 2010.

McGowan appeared in Skins in February 2011. He played Nick’s coach in the fifth episode of the new series. On 12 March 2011 he played the part of the Pirate King in Gilbert and Sullivan’s The Pirates of Penzance, at the Barbican Hall, London. and, later in the year, took over from Rupert Everett the part of Henry Higgins in Pygmalion at the Garrick Theatre, opposite Kara Tointon as Eliza Doolittle. In April 2011, he took to the stage at the Djanogly Theatre, Lakeside Arts Centre at the University of Nottingham in David Mamet’s controversial drama Oleanna. Also in 2011 he co-starred in the CBBC series Leonardo as Piero di Cosimo de’ Medici. On 9 June 2011 he was unveiled as the newest addition to the BBC Wimbledon commentary team.

In June 2011 it was announced that McGowan had become a Patron of the Friends of Brandwood End Cemetery, where over 30 members of his extended family are interred.

McGowan is a supporter of Leeds United, even claiming that he decided to study at Leeds partly because of its proximity to Elland Road, and Coventry City, the team closest to the area where he spent his late teens, and his interest in football forms the basis of his 2009 book A Matter of Life and Death. On 17 December 2012 edition of Countdown, Susie Dent revealed that McGowan neither owns a car nor drives.

McGowan was in a relationship for seven years with fellow television comedian Ronni Ancona. In August 2013 McGowan married his girlfriend Charlotte Page alongside whom he had performed in The Mikado.

In 2013 McGowan embarked on a fifty-date stand-up tour in his show Not Just A Pretty Voice. He also took part, with Eddie Izzard, in the first ever stand-up show performed by two English comics totally in French in Sheffield. His voice appeared in the film The Unbeatables.

In 2013 McGowan explained in a piece for The Guardian that he had “… hero-worshipped the French composer Erik Satie for many years. Not only was he a hugely innovative and visionary composer – but he was also a man with a passion for all forms of art.”

In October 2014 McGowan narrated, in the guise of Satie, a concert of surrealist ballet music from Paris in the 1920s, given by the BBC Concert Orchestra at the Queen Elizabeth Hall in London and broadcast live by BBC Radio 3.

In September 2017 he released a debut album on Sony Classical. featuring piano performances of several short classical pieces, all chosen and learned by him. Previously McGowan could only ever play two pieces, but then practised for up to six hours a day, over a nine-month period, despite already being in his early 50s.