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Her university education was at Somerville College, Oxford. (Somerville at that time was a women's college, known in Oxford as "the bluestocking college".) There she read Greats (the Oxford term for traditional courses in the humanities, with emphasis on the ancient classics of Greece and Rome, including philosophy).
The drug smuggler Howard Marks was a student at Balliol College, Oxford while Frances was at Somerville. In his autobiography Mr. Nice he describes her as "vivacious". The book contains an anecdote of Marks taking LSD for the first time before visiting Frances in her rooms. While they sat listening to The Rolling Stones, Marks described to her the trip he was experiencing.
In 1970 she started work as an Assistant Editor at the London publishing firm of Studio Vista. She went on to become its Managing Director. From Studio Vista she moved to a job with the publisher Marshall Cavendish, and from there to Weidenfeld and Nicolson, where she was given her own imprint.
A story that followed her throughout her career, often passed on from employees to new recruits, was of the staff-walkout and demonstration she headed while at Studio Vista in 1975. This was a protest against redundancies proposed by Collier Macmillan, the firm that had come to own Studio Vista. The protest went on for a number of days, and is described as a strike. It achieved concessions from Collier Macmillan. (The story itself is striking for the incongruity between the shy and reserved bluestocking figure of Frances Lincoln, and the tale's casting of her in the role of "strike leader".)
In 1977 Frances went out on her own as an independent publisher/packager, publishing both under her own name and in co-editions. The firm she founded continues as Frances Lincoln Publishers, based in London. The firm is known for the list of illustrated gardening books it publishes, and for the illustrated children's books that it began publishing from 1983, many of which have won awards and prizes. In Frances's time, her firm was notable for employing an almost exclusively female staff.
Frances Lincoln died from pneumonia at age 55 in 2001.
Frances married John Nicoll, the author of the first book she had commissioned. (He later headed Yale University Press in the UK). The couple had a son and two daughters.