Agutter was born in Taunton, Somerset. The daughter of Catherine Kit Lynam and Derek Brodie Agutter, a British Army officer, she travelled the world as a child. Her first film appearance was in

She first came to the attention of television audiences as Roberta in a BBC dramatisation of , and went on to play the same part in Lionel Jeffries' 1970 film of the book. Her quality of ingenuousness led on to a more serious role in (1971), playing a teenaged schoolgirl who was lost in the Australian outback with her younger brother. The film's theme of the transition from childhood to adulthood mirrored Agutter's life and career at the time.

Agutter appeared in a number of films over the next decade, including: (1981).

In the last decade, Agutter has mainly worked in television. She has appeared in the TV series , this time playing the role of the mother. Since 2002, Agutter has been featured in the British television series

Agutter is married to Johan Tham, a Swedish hotelier. The couple have one son, Jonathan. The family lives in Cornwall, England.