McKee was born in Peterlee, County Durham, the daughter of a coal miner, and grew up there and in nearby Easington and Sunderland. Her first experience of acting occurred in her final year at primary school where her teacher finished the school week off with improvisations. Seeing a poster in a shoeshop window for a new youth drama group, McKee and her friends decided to attend, initially not seriously but later becoming enthusiastic. It led to McKee's first professional appearance, working on Tyne Tees children's series, Quest of Eagles.
From the age of 15, McKee spent three summers in London with the National Youth Theatre.After completing her A-Levels at East Durham College, she decided, with her parents' blessing, to apply to drama schools rather than art colleges. However, she was rejected by Bristol Old Vic Theatre School, London Academy of Music and Dramatic Art and the Central School of Speech and Drama.
McKee has been married to Kez Cary since 1989; they live in East Sussex, England. She has been a vegetarian since 1982.
In 2002, McKee was awarded an Honorary Doctorate of Arts from the University of Sunderland, receiving the honour alongside footballer Niall Quinn.
