Mafham began his career at The Royal Shakespeare Company in 1990. He was with the RSC for four years.

Mafham first came to prominence when he played Nigel Hawthorne's emotionally damaged son Daniel Pascoe in Paula Milne's The Fragile Heart. The drama was screened on Channel 4 in the UK in 1996. It won the 1997 BAFTA award for Nigel Hawthorne as Best Actor, and was nominated for several awards including Best Drama Serial. It was also nominated in the Royal Television Society awards that year.

Mafham played Mortimer Lightwood in the BBC's 1998 adaptation of Charles Dickens' Our Mutual Friend. Much of the story is seen from Mortimer's perspective. Our Mutual Friend was acclaimed worldwide, and won four BAFTAs including Best Serial. It was nominated for four more BAFTAs, as well as awards from the Royal Television Society, the Broadcasting Press Guild and the San Francisco International Film Festival. In 1999 he played Grahame Tranter in the Midsomer Murders episode "Death of a Stranger."

The Clinic was a multi award winning prime time Sunday night drama for RTÉ in Ireland. It has been sold all over the world. It ran for seven seasons from 2003-2009, regularly gathering an audience share of over 40%. The show was widely praised in the media. Mafham played the womanising, scheming and manipulative English plastic surgeon Dan Woodhouse. He appeared in every episode.

In February 2010, Mafham guest presented The Afternoon Show, RTÉ television's flagship daytime show.

In 2011 Mafham set up the production company InSite Films, which produces a range of video content including music videos, promotional films and documentaries.

Mafham appeared in the Big Finish audio Companion Chronicle adventure The Jigsaw War which was a two hander with Frazer Hines. He featured in the fourth Doctor adventures with Tom Baker, The Dalek Contract and The Final Phase, released in June and July 2013.

On 6 June 2014 Mafham took part in the BBC Radio 2 D Day 70th anniversary concert at the Royal Albert Hall. The concert was broadcast live on Radio 2 and at over 150 cinemas across the UK. The event was presented by Dermot O'Leary, Jeremy Vine and Louise Minchin. Sir Patrick Stewart read Churchill.

In spring 2015 Mafham played Antonio in The Merchant of Venice at Shakespeare's Globe Theatre. Jonathan Pryce played Shylock. The production was revived for a major tour in 2016, visiting New York, Washington and Chicago in the U.S. and several cities in China before returning to Shakespeare's Globe in Octoberand culminating in a run in Venice at the Teatro Goldoni. The production received rave reviews.

In February 2016 he appeared in the BBC TV series Father Brown as Sir Malcolm Braithwaite in episode 4.6, "The Rod of Asclepius".

In autumn 2017 Mafham appeared in King Lear (as Albany), at the Chichester Festival Theatre. Ian McKellen played Lear and featured Sinead Cusack as a female Kent. The production received rave reviews, and Mafham's performance described as "revelatory" in the Daily Mail. The production is thought to be transferring to the West End in 2018.