Marchant, whose his father was a printer and mother a school dinner lady, was born and raised on a council estate in Wapping in the East End of London, which he has described as, "a very hard, heavy place to live sometimes." He has stated that while estates have changed since he grew up on one, the poverty is still the same and it hasn't gone away. He was educated at St Joseph's Academy, Blackheath and went on to become a London boxing champion and a member of the England boxing squad.
Inspired by, "the DIY ethic of the Jam and the Clash," he got his start in writing at the age of 18, when a selection of poems he had submitted to Riot Stories, an imprint established by Jam musician Paul Weller, were published.
His big break came in 1980, when his first play Remember Me?, which he had submitted to 20 theatres, was accepted and staged by the Theatre Royal Stratford East in London, an experience which he likens to winning the lottery. It was at this point that he ceased pursuing a career in heavyweight professional boxing, although, "getting punched in the face," was, he has claimed, "very good preparation for being a writer."
His second play London Calling, which took its name from a song by the Clash, was combined with Dealt With for the double bill Thick As Thieves, produced at the Theatre Royal Stratford East's The Square Thing studio theatre in 1981. Looking back on his early career he has stated that at the time he wondered if he were part of, "some sort of liberal social engineering," which advantaged him as an ex-boxer from a council estate with no university education.
His next two productions, Stiff and Raspberry, were put on at the Soho Poly in 1982. That same year The Lucky Ones was staged at the Theatre Royal Stratford East and later re-staged at Islington's The Old Red Lion in 1986. These productions won him the London Critics' Theatre Award for Most Promising Playwright that year.
Welcome Home, Marchant's play about a squad of Falkland War veteran paratroopers meeting up to act as pall-bearers for one of their squad killed in the war, debuted at Hemel Hempstead's Old Town Hall Arts Centre before being taken on a nationwide tour by Paines Plough which concluded at the Royal Court Theatre in 1983. It was later re-staged at The Old Red Lion in 1989.
BBC Television's production of Raspberry in 1984 gave Marchant his break in television. He credits the smooth transition that he and his generation had into screenwriting to the vogue for televised plays during these decades.
Straddling theatre and television with Lazydays Ltd., produced at the Theatre Royal Stratford East in 1986, followed by London Weekend Television's broadcast of The Moneymen in 1987, he has stated a preference for the theatre due to the feedback from a live audience, but his survival in the industry has been credited to his move to television.
Marchant's final theatrical works to date consisted of The Attractions produced at Soho Poly, which was published by Amber Lane Press the following year, Marty Cruickshank produced at the Royal Court Theatre's Theatre Upstairs, and Speculators produced by the Royal Shakespeare Company at the Barbican Centre's The Pit, all in 1987.
The BBC Television productions of Death of a Son for Screen Two, The Attractions for Screenplay, and the three-part miniseries Take Me Home, marked his permanent move into television in 1989.
Methuen Drama, an imprint of Bloomsbury Publishing, released a compilation volume, consisting of the scripts for Welcome Home, Raspberry and The Lucky Ones in 1996.
He has also written the comedy film Different for Girls.
He appeared on University Challenge (BBC Two) in a special actors-versus-writers episode in January 2006.
He was featured in the writers section of the Broadcast magazine Hot 100 2006.
In 2007 he wrote an ITV series, Whistleblowers, for ITV, and an award-winning single film, Mark of Cain for C4.
In 2008, David Tennant starred in a BBC1 single film, Recovery, in which Marchant explored the aftermath of brain injury on a man's life and family.
In 2009 he wrote the teleplay for the CBC Television movie Diverted starring British actor David Suchet and Canadian actor Shawn Ashmore. This drama centred on the impact the September 11th, 2001 terrorist attacks had on the town of Gander, Newfoundland as hundreds of flights were forced to land outside American airspace.
He wrote episodes for all 3 series of Garrow's Law, the film The Dig and, broadcast in 2012, the hard-hitting drama about the British probation service Public Enemies, all for BBC1.
Marchant received an Honorary Doctor of Letters from the University of Hertfordshire during a ceremony at the Cathedral and Abbey Church of St Alban on November 16, 2011. This was awarded, according to the university, "in recognition of his commitment to creative ambition and integrity in British drama."
He was resident writer at the Royal National Theatre.