One of Carmichael's paternal great-grandfathers was aviator Captain Norman Blackburn, a British pilot and flying instructor during the First World War, and afterwards a Director of Blackburn Aircraft. She was educated at Shirley Junior School, The Mountbatten School, and Peter Symonds College. Carmichael attended the Bristol Old Vic Theatre School in Bristol, graduating in 2007, before spending two years in various odd jobs, including a teaching assistant, receptionist, and nanny while going to tiny auditions in fringe theatres.
She played Laura in Reasons for Living as part of the 2009 Scratch Festival at Battersea Arts Centre. In late 2009, she played Miranda in a touring production of Shakespeare's The Tempest.
Carmichael lives in Camden, London. Prior to landing the role of Lady Edith Crawley in early 2010, Carmichael had worked as a secretary in a doctor's surgery.
Carmichael's previous substantial role was in 2011, in David Hare's Plenty at the Sheffield Crucible Theatre with co-stars Anna Friel as Yelena and Ken Stott as Vanya.
Carmichael made her West End debut in Uncle Vanya opposite Anna Friel and Samuel West in October 2012. She played Arabella in The Fitzrovia Radio Hour at The Underglobe Theatre in early 2013.
Carmichael stars in the 2015 British black comedy feature film Burn, Burn, Burn, a coming-of-age tale, inspired by the Jack Kerouac novel On the Road published in 1957. The directorial debut of Chanya Button, it follows the fictional story of two girls, Seph (Carmichael) and Alex (Chloe Pirrie), taking a road trip to follow the instructions of their close friend Dan, who has died and given them instructions where to scatter his ashes. The ashes (stored in tupperware in the glove compartment) keep diminishing in quantity as the trip progresses. The film had its World premiere at BFI London Film Festival 2015.
In 2016, Carmichael played Madam in Jamie Lloyd's production of The Maids at the Trafalgar Studios in London's West End, co-starring Uzo Aduba.
