Heap was born in Tamil Nadu, India, to an English father and American mother, the youngest of four boys. He began his acting career in the 1980s as a member of the Medieval Players, a touring company performing medieval and early modern theatre, and featuring stilt-walking, juggling and puppetry. His brother, Carl Heap, was the artistic director of the company. After its demise, he became part of the street theatre duo The Two Marks (with Mark Saban) who appeared on television shows Ghost Train and 3-2-1.
He has appeared in a variety of television comedy roles, often playing obsessive and self-deluded characters, including struggling artist Brian Topp in Spaced, the pompous Dr. Alan Statham in Green Wing, and various roles in the sketch show Big Train, many scenes of which he improvised. He has worked in a number of ventures with Chris Morris, appearing in Jam, its radio predecessor Blue Jam, and the documentary parody series Brass Eye. He voiced the lead character of Eric Feeble in the animated comedy Stressed Eric. Other recurring roles included Terry Roche in Paul Whitehouse's comedy-drama Happiness and Derek Few in How Do You Want Me?. Heap played Harry in the short-lived Rob Grant TV series The Strangerers, aired in 2000. He also guested in the second series of the BBC comedy Look Around You as Leonard Hatred.
He appeared in the 2007 BBC One drama Hotel Babylon as an unsuccessful businessman who became a bellboy. Between 2008 and 2010 he appeared in 32 episodes of the BBC period drama Lark Rise to Candleford as head postman Thomas Brown, as well as super villain Lightkiller in an episode of the sitcom No Heroics. He also appears as the father of Chris Miles in the Channel 4 programme Skins. Heap played the love interest of the main character in the second series of the BBC comedy Love Soup. He played the role of Charles Dickens in the 2009 BBC Two drama Desperate Romantics. Also that he played Jessica Hynes' husband in the one-off comedy Lizzie & Sarah, written by Hynes and Julia Davis.
In 2010 Heap appeared as Bob Stevens, the leader of a rambling group in the BBC4 series The Great Outdoors. He also appeared as a psychiatrist in Miranda Hart's comedy Miranda on BBC2. In October 2010 he appeared as Robin in the four-part BBC drama Single Father. Heap plays Jim in the Channel 4 sitcom Friday Night Dinner alongside Simon Bird and Tamsin Greig. He also played Andrew Thorogood in the BBC Four comedy Holy Flying Circus and Jonas in the 8th episode of E4's sci-fi comedy-drama Misfits series 3.
He joined the cast of the Sky1 original series Spy for its second season commencing in October 2012, replacing Tom Goodman-Hill as Philip Quil, Judith's partner and Marcus' headteacher. He appeared in the spin-off episode of Outnumbered, the Christmas special episode, aired on 24 December 2012 in which he portrayed Norris, for this single episode. He played the owner of a pet crematorium in Sue Perkins's 2013 comedy Heading Out. Mark also had a leading role in BBC Radio 4's adaptation of Gogol's 'Lost Souls.' He starred as Robert Greene in three seasons of Upstart Crow (2016–2018), a BBC 2 sitcom about Shakespeare, written by Ben Elton. His co-stars included David Mitchell, Harry Enfield, Rob Rouse, Gemma Whelan and Liza Tarbuck.
In 1983, Heap made a brief appearance as a fire-breather in the James Bond film Octopussy. He played a school teacher in the 2002 film About a Boy. He appeared in Tim Burton's 2005 Charlie and the Chocolate Factory. He played supporting roles in Confetti (2006), Tunnel of Love (2004), Stardust (2007), and The World's End (2013). In 2008 he co-starred in the surreal science fiction film Captain Eager and the Mark of Voth.
|1997||Bring Me the Head of Mavis Davis||Duncan|
|2002||About A Boy||Maths teacher|
|2008||Captain Eager and the Mark of Voth||Scrutty Baker|
|2018||The Midnight Gang||Sir Quentin||TV Movie|
|1987||The Les Dennis Laughter Show||The Two Marks||1 episode|
|1990||Up Yer News||Film Assistant||1 episode|
|1992||Packing Them In||Fire eating stiltwalker||1 episode|
|1993||Viva Cabaret||The Two Marks||1 episode|
|1994||The Bill||Chris Boxer||1 episode|
|Seaforth||Capt. Karl Von Berner||2 episodes|
|How High The Moon|
|1995||The World of Lee Evans||Platform Guard||1 episode|
|1997||Hospital||Dr. Ralph Crosby|
|An Unsuitable Job for a Woman||DS Maskell||1 episode|
|1997–1998||Smith and Jones||2 episodes|
|1997–2001||Brass Eye||Various roles|
|1998||Kiss Me Kate||Peter||3 episodes|
|1998–1999||How Do You Want Me?||Derek Few|
|1998–2000||Stressed Eric||Eric Feeble|
|1998–2002||Big Train||Various roles|
|1999||All Along the Watchtower||Mr. Carter||1 episode|
|People Like Us||Graham Atkinson||1 episode|
|2001||The Ultimate Stress Show: Managing Stress|
|2003||Doc Martin and the Legend of the Cloutie||Mitch|
|Spine Chillers||Balfus||1 episode|
|2004||Dalziel and Pascoe||Julian Finch||1 episode|
|The Calcium Kid||Sebastian Gore-Brown|
|Swiss Toni||Terry Fragment||1 episode|
|Tunnel of Love||Gibson|
|Out of Time||Charlie|
|2004–2006||Green Wing||Alan Statham||17 episodes 1 special|
|2005||Blake's Junction 7||Avon||Short|
|Look Around You||Leonard Hatred||2 episodes|
|Casanova||Doctor Gozzi||1 episode|
|Charlie and the Chocolate Factory||Man With Dog|
|2007||Hotel Babylon||Robert Kane||1 episode|
|Marple: At Bertram's Hotel||Mr. Humfries|
|2008||Skins||Graham Miles||1 episode|
|Love Soup||Douglas McVitie|
|No Heroics||Lightkiller||1 episode|
|2008–2011||Lark Rise to Candleford||Thomas Brown|
|2009||Desperate Romantics||Charles Dickens|
|Cast Offs||Darren||1 episode|
|2010||Lizzie and Sarah||Michael|
|The Great Outdoors||Bob|
|Fable III||Brian||Video game|
|2010, 2015||Miranda||Anthony||2 episodes|
|2011||Holy Flying Circus||Andrew Thorogood|
|2011–present||Friday Night Dinner||Jim Bell||31 episodes|
|The Indian Doctor||Rev Herbert Todd|
|A Moody Christmas||Heathrow Passenger||1 episode|
|Is This a Joke?||Short|
|2012–present||The Increasingly Poor Decisions of Todd Margaret||Lord Mountford||4 episodes|
|2013||Heading Out||Brian||1 episode|
|All Stars||Simon Tarrington|
|The World's End||Publican 7|
|Midsomer Murders||Simon Fergus-Johnson||1 episode (series 16 episode 1)|
|2014||Death in Paradise||1 episode (series 3 episode 6)|
|2015||We're Doomed! The Dad's Army Story||Clive Dunn|
|2016–present||Upstart Crow||Robert Greene|
|2016||The Comedian's Guide to Survival||Pick Up Driver|
|Endeavour||Felix Lorimer||1 episode (series 3, episode 4)|
|2017, 2018||Benidorm||Malcolm/Dennis||3 episodes (series 9, episodes 7 and 8 and series 10, episode 7)|
In 2008 Heap played the role of Widmerpool in a Radio 4 serialisation of Anthony Powell's A Dance to the Music of Time. He played Eliza's husband in 2006 Radio 4 play The Eliza Stories and appeared as Marmite the Dwarf in the short-lived Radio 4 sitcom The Sofa of Time. He starred in the music video for Four Tet's single "Smile Around the Face" in 2005, contributed a multitude of character voices in the audiobook "Do Ants Have Arseholes?". In 2012 he starred as Martin in the Radio 4 play Cordite for Breakfast, a comedy about Napoleonic-era battle re-enactments. In March 2013, he appeared as Rincewind in a 4-part Radio 4 adaptation of Terry Pratchett's Eric. In 2014 it was announced that Heap will play the angel Aziraphale in the BBC radio adaption of Neil Gaiman and Terry Pratchett's Good Omens.
- "Mark Heap". IMDb. Retrieved 5 October 2008.
- Carl Heap. "Finding the method in medieval theatre's madness | Stage". The Guardian. Retrieved 25 January 2016.
- "Big Train at 20 - interview with Arthur Matthews". The Digital Fix. 23 July 2018. Retrieved 13 August 2018.
- Wilmore, James (7 May 2010). "Old Speckled Hen renews sponsorship of TV channel Dave". The Publican magazine. Retrieved 15 April 2011.
- "Cordite for Breakfast". BBC. 10 July 2010. Retrieved 5 December 2012.
- Brown, Brigid (5 September 2014). "BBC Radio Brings Neil Gaiman and Terry Pratchett's Good Omens to Life". BBC America. Retrieved 6 September 2014.