Quesnel was born and raised in Eccles, Lancashire, along with her six siblings.. Her father was born in Trinidad. She read English at Oxford University before spending a year at drama school. In the 1980s she performed in Humphrey Carpenter's Vile Bodies band at the Ritz Hotel, and performed in a tribute concert to him following his death in 2005. In 2003, she began screenwriting, producing scripts for Doctors and Family Affairs, appearing in the latter as Diane Short.
She played Dr Monica Broome in the first series of Cardiac Arrest and DC Grace Harris in the first two series of Thief Takers. She had a recurring role in the third series of Cold Feet as Emma Keaton and returned to medical dramas in 2006, playing Dr Christine Whelan in The Golden Hour. In 2007 she starred as Nita in the BBC One series True Dare Kiss, and later that year began a recurring role in EastEnders as Rachel Branning, taking over the character from Sukie Smith. In February 2008 she played the spoken title role in a City of Birmingham Symphony Orchestra production of Stravinsky's Perséphone, broadcast on BBC Radio 3. In July 2008, she appeared in an episode of the ITV murder mystery series, Midsomer Murders as Journalist Julie Benson, and in an episode of George Gently entitled "The Burning Man", playing the character Wanda Lane. In March 2010 she appeared as Maureen in BBC One's second series of Five Days. She also played the spaceship captain in the Doctor Who' 2010 Christmas special, "A Christmas Carol". In November 2010 she appeared as Christopher Eccleston's character's wife in Jimmy McGovern's Accused. She has also played a pregnant woman in an episode of Not Going Out. She played the character of Olga Fitzgerald, Geography Teacher and Headteacher Vaughn Fitzgerald's estranged wife in BBC's Waterloo Road, in 2015. She currently plays a part in BBC's The A Word, and the role of Dorothea Ames, Head Teacher at Coal Hill Academy, in the BBC3 series Class. In 2016 she provided the voice of Yuria of Londor in the video game Dark Souls III