Clarissa Dickson Wright was born in St John's Wood in London. The youngest of four children, she was given 11 forenames. Her father, Arthur Dickson Wright, was a surgeon to the Royal Family, and her mother, Molly, was an Australian heiress. Her cousin is comedian Alexander Armstrong. Born to a wealthy family, she had a Catholic childhood and grew up in a nine-bedroom house in St. John's Wood that was staffed with several servants. Dickson Wright's father was an alcoholic who subjected his wife and children to verbal and physical abuse continuing into Clarissa Dickson Wright's adulthood, although this is a claim that her older sister Heather has always denied. At the age of 11, Clarissa Dickson Wright was sent to Sacred Heart School, a boarding school in Hove, East Sussex. After school she studied for the Bar at Gray's Inn, while pursuing a law degree at University College London. At the age of 21, Dickson Wright passed her exams and became the country's youngest barrister. After her mother died of a heart attack in 1975, she inherited £2.8 million. Her mother's death, combined a few years later with her father's, left her in a deep depression, and she drank heavily for the following 12 years.

In 1979, Clarissa Dickson Wright took control of the food at a drinking club in St James's Place in London. While there she met Clive, a fellow alcoholic, and they had a relationship until his death in 1982 from kidney failure at the age of 40. Shortly thereafter she was disbarred for practising without chambers. Dickson Wright claims that, during her alcoholic years, she had sex with an MP behind the Speaker's chair in the House of Commons. By 1983, she was homeless and staying with friends. For two years she was cook-housekeeper for a family in Sussex until she was fired for her alcohol-induced behaviour. After being charged with driving under the influence, Dickson Wright started to attend Alcoholics Anonymous meetings, counselling, and a detox centre. In 1987, she attended a recovery centre called Promis in Kent; she left after 10 weeks.

Seven months after leaving Promis, Dickson Wright offered to run Books For Cooks, a shop and cafe in Portobello Road, London, for the shop's owner. After seven years, the owner decided to sell the shop, and as Dickson Wright did not have the money to buy it she was sacked. She then moved to Edinburgh and ran the Cooks Book Shop.

During her time in Edinburgh, television producer Patricia Llewellyn asked her and Jennifer Paterson if they wanted to make a television programme; they made a pilot in autumn 1994. After the pilot, BBC2 commissioned a series of Two Fat Ladies. Three successful series were made and shown around the world. Paterson died in 1999 mid-way through the fourth series.

Two Fat Ladies ended after Paterson's death. Dickson Wright appeared with Johnny Scott in Clarissa and the Countryman from 2000 to 2003 and played the gamekeeper in the sitcom Absolutely Fabulous in 2003. In 2005, Dickson Wright took part in the BBC reality television show Art School.

Dickson Wright has campaigned for the Countryside Alliance and was the first female Rector of the University of Aberdeen. Her autobiography, Spilling The Beans, was published in September 2007. In 2008, she presented a one-off documentary for BBC Four, Clarissa and the King's Cookbook, where she makes recipes from a cookbook dating to the reign of Richard II.

Along with racehorse trainer Sir Mark Prescott, Dickson Wright was charged under a private prosecution by the International Fund for Animal Welfare with an offence under the Hunting Act 2004, namely hunting hares with dogs in North Yorkshire in March 2007. On 1 September 2009, Dickson Wright and Prescott pleaded guilty and received an absolute discharge at Scarborough Magistrates' Court. They said that they were invited to the event by the Yorkshire Greyhound Field Trialling Club, who told the court they believed it was running a legal event by using muzzle dogs.