In 1982, McGovern started his TV career working on Channel 4's soap opera Brookside. He tackled many social issues in the course of the series, especially unemployment – which was at a post-war high at the time. In 1993, he created the drama serial Cracker, about the work of a fictional Criminal Psychologist played by Robbie Coltrane. Made by Granada Television and screened on ITV, the series was a critical and popular success, lasting until 1995. Cracker also aired in the United States, on the Arts and Entertainment cable network. McGovern's writing earned him two Edgar Awards from the Mystery Writers of America. In 1997 he created The Lakes, a drama that shared Brookside's realist setting and reused themes from Cracker, such as gambling addiction. In 2006, he created the BBC One drama, The Street; its third and final season aired in 2009.

McGovern wrote the screenplay for the 1994 drama, Priest.

McGovern also wrote the script for the television docudrama Hillsborough (1996), based on the events of the stadium disaster in 1989, which claimed the lives of 96 Liverpool fans at an FA Cup semi-final. Among the cast of this drama was Christopher Eccleston, who also featured in Cracker, along with former Brookside actor Ricky Tomlinson.

McGovern has described cinema scriptwriters as being treated like hacks and forced to crank out countless drafts by successive producers. McGovern has openly criticised dramas such as Footballers' Wives, lamenting the lack of quality, believable storytelling in the early 2000s.

McGovern wrote the book for the musical stage show King Cotton, which explores links between the transatlantic slave trade and industrialisation in North West England, as part of the Liverpool European Capital of Culture 2008. King Cotton premiered at the Lowry in September 2007 before moving to the Liverpool Empire.

In 2009, McGovern was the executive Producer on the BBC One miniseries Moving On.

His series Accused aired from 2010 to 2012 on BBC One. It followed a similar format to The Street but with a crime component. The series' Writers included McGovern, Danny Brocklehurst, Alice Nutter and Shaun Duggan. It was produced by Sita Williams.

In 2012, McGovern together with local Indigenous Australian Writers from Sydney, developed the Australian television drama series Redfern Now, set among the Indigenous Australians of the Sydney suburb of Redfern. The six-part series follows a similar format to Accused, telling the stories of six inner-city households in one street whose lives are changed by a seemingly insignificant incident. The series debuted on 1 November 2012, was produced by Blackfella Films, and has already been commissioned for a second series.

He believes that television Directors are underrated. He says: "I have worked twice with David Blair" on The Lakes and The Street, "and I can tell you that he is the best there is. He can make a good project great... Why David hasn’t won the acclaim he deserves is a mystery to me".