Carvel was born in Marylebone, London, the son of a Psychologist mother and John Carvel, a Journalist. Carvel was educated at University College School. He gained a first class honours degree in English at the University of Sussex, then won a place at the Royal Academy of Dramatic Art (his acting training was paid for via scholarships from The Wall Trust and the Sir John Cass Foundation), graduating in 2003 after a three-year course.
Carvel has appeared in Revelations at the Hampstead Theatre, Rose Bernd at the Arcola Theatre, as Alexander Ashbrook in the 2005-2006 and 2006-2007 Royal National Theatre productions of Helen Edmundson's Coram Boy, in The Life of Galileo at the National Theatre, The Man of Mode at the National Theatre, Parade at the Donmar Warehouse and Matilda the Musical at the Cambridge Theatre, produced by the Royal Shakespeare Company.
Carvel was nominated for the Olivier Award for Best Actor in a Musical for his performance in Parade in 2008. He won the award in 2012 for his performance as Miss Trunchbull in Matilda the Musical, a production that won six other Oliviers. Carvel also won the UK's TMA Award for Best Performance in a Musical and was similarly nominated for the London's Evening Standard Award. He played Enrico in Damned By Despair at the National Theatre.
In March 2013, he reprised his role as Miss Trunchbull in Matilda on Broadway at the Shubert Theatre. This won him a Drama Desk Award for Outstanding Featured Actor in a Musical and a nomination for Tony Award for Best Actor in a Musical, one of only a handful of nominations for an actor portraying a character of the opposite sex.
In 2015, Carvel starred as Jonathan Strange in the BBC One adaptation of Susanna Clarke's novel Jonathan Strange & Mr Norrell, opposite Eddie Marsan as Gilbert Norrell. He played Nick Clegg in the Channel 4 drama Coalition and in September appeared as the unfaithful husband of Suranne Jones's title character in the BBC One thriller series Doctor Foster. The second series of Doctor Foster started filming in September 2016 and started broadcast in September 2017.
In February 2016, Carvel announced his directorial debut. He directed the play Strife at the Minerva Theatre, Chichester, which opened in August 2016.
In September 2017, Carvel played the role of Rupert Murdoch in the play "Ink" by James Graham.
