He married his childhood sweetheart who supported his ambition to be a professional actor, and this early marriage broke down as he pursued his acting ambitions. In 1974, he joined the Liverpool Everyman Theatre Company, where he met his second wife, remaining with the company for eight years.

Costigan has been on television since 1978. He starred in the 1982 series of The Barchester Chronicles, an adaption of the novels by Anthony Trollope, in which he played the part of Tom Towers. In 1984 he appeared as Philip the Bastard in the BBC Television Shakespeare production of The Life and Death of King John (alongside Leonard Rossiter in the title role).

He rose to fame in 1986 as adulterous businessman Bob in the comedy film Rita, Sue and Bob Too. He has since starred or featured in many television productions, including The Adventures of Sherlock Holmes (providing mellifluous Peter Lorre-type villainy) Kavanagh QC, Coogan's Run, Connie, A Touch of Frost, Inspector Morse, Murder Most Horrid, So Haunt Me, London's Burning, The Bill, Holby City, The Long Firm, Vera, Dalziel and Pascoe, The Ruth Rendell Mysteries, The Inspector Lynley Mysteries, The Beiderbecke Connection, New Tricks and Casualty. His film work includes Calendar Girls and Shirley Valentine.

His partner is the Writer Julia North, with whom he wrote a 1990 episode of Birds of a Feather. They have three sons – Niall (who is also an actor), and two others.

He has appeared in the role of Max Capricorn in the 2007 Doctor Who Christmas special, Voyage of the Damned.

In the theatre, he created the role of Mickey Johnstone in Willy Russell's musical Blood Brothers, originally at the Liverpool Playhouse, and later at the Lyric Theatre, London. He most recently played the role of Estragon in Samuel Beckett's play Waiting for Godot at the Manchester Library Theatre for three weeks from 16 February to 8 March 2008, and played Willy Loman in Arthur Miller's Death of a Salesman at York Theatre Royal in November 2008. In December 2009, it was announced that he is to join Emmerdale as a friend of Rodney Blackstock. He made his debut in the soap in March 2010 and his last appearance was shown on 23 July 2010. On 4/5 April 2010, he starred as Alan, the ex-husband of Christine, Inspector Frost's new love interest in A Touch of Frost. In 2012 he appeared in william Shakespeare's King Lear at the Citizens Theatre, Glasgow, alongside David Hayman. In 2014, he appeared in Happy Valley. He resumed the role, Nevison Gallagher, in the 2016 series. He also starred in the hit TV series Line of Duty as Patrick Fairbank.

In July 2016 he played Sir Ethelred in the BBC's 3-part television adaptation of Joseph Conrad's 1907 novel The Secret Agent.

His first novel ‘The Single Soldier’ is available from Spring 2017. Published via Urbane Publishers.