Simpson was born in Dublin, Republic of Ireland. His father is Irish and his mother was of Greek-Rwandan descent. His father met his mother in Rwanda whilst training to be a teacher.
When Simpson was a child he visited Rwanda with his mother.
His mother"s first language was Kinyarwanda. After his parents divorced, he moved to London with his mother and his sister, Fiona, where he has lived ever since.
He played Karim in the film adaptation of Monica Ali"s novel Brick Lane. Simpson lived in Dublin until he was six years old. When Simpson was at primary school, he began attending drama classes on Thursday evenings with an amateur dramatics club
In 2002, Simpson played twins, Magid and Millat, in White Teeth.
In 2003, he starred in Second Generation, and appeared in State of Play. In 2003, Simpson played a supporting role in Code 46.
In 2004, he played the role of Hassan Sabbah in The Keeper: The Legend of Omar Khayyam. In 2005, he appeared in Chromophobia.
In 2006, he played a supporting role in Mischief Night.
In 2007, he played the lead role of Karim in the film adaptation of Monica Ali"s novel Brick Lane, and a supporting role in Exitz. Simpson had one week to learn the part of Karim for Brick Lane. In 2008, Simpson was a British Independent Awards jury member.
In 2006, Simpson played the role of Dionysus in Conall Morrison"s The Bacchae of Baghdad (an updated version of Euripides"s play The Bacchae) at the Abbey Theatre.
In 2011, he played the role of Maz in John Donnelly"s The Knowledge, and the role of Parvez in Steve Waters" Little Platoons, both at the Bush Theatre. In 2008, whilst he was artist-in-residence with creative arts group Metal Simpson completed a song cycle, Very Present Tense.
He wrote it over a number of years in response to the death of his mother. The songs which reference musical idioms including blues, jazz and Rwandan folk, reflecting his Rwandan and Irish family heritage, have been developed in collaboration with composer, Tom Havelock.
On 8 August 2008, the song cycle premiered at the arts hub in Edge Hill Station pavilion, during the Liverpool European Capital of Culture.
On 29 September 2009, he performed the work for the second time with Metal at the Village Green Festival, this time working with a group of musicians from Southend. Simpson then worked on recording the work.
