Francis Cook was educated at Bradfield College, Reading. He later studied under Harold Speed from 1926-1932, Arnesby BROWN between 1932-1934, and Samuel John Lamorna BIRCH in 1935-36. Flower paintings were a speciality.

An only child, he had been born into an extremely wealthy family. His great-grandfather had acquired an impressive collection of Old Masters, which was augmented by artworks purchased by Francis's father, Sir Herbert Cook. Herbert's expertise led to his becoming a co-founder of The Art Fund, and the Burlington Magazine in 1903, later becoming a trustee of the National Portrait Gallery and of the National Gallery. Subsequent to World War I, Sir Herbert suffered significant financial losses, which were exacerbated by the Wall Street crash of 1929. In 1934 thirty paintings from the family collection were set aside for Francis.

In 1939, on the death of his father, Francis came into his title, and moved to one of many family properties, Porthallow Old House, Talland Bay, Looe in 1940. Music and art history were very important to him, and he lived an unconventional and colourful life, marrying seven times.

He exhibited successfully at the Royal Academy twice, in 1936 and 1938. As a result of his association with Arnesby Brown and Lamorna Birch, he was known to the west Cornwall art fraternity, becoming an associate member of STISA in 1940. The first work which he showed there was 'Cornish Studio - Winter Sunshine' which was highly praised. During the early 1940s he completed a series of religious paintings.

In 1947 Sir Francis moved to Jersey for financial and tax reasons. All of his properties in England and Portugal were sold and Porthallow Old House became the Talland Bay Hotel.

Around 1200 of his paintings are now owned by the Jersey Heritage Trust, and a selection displayed in the Sir Francis Cook Gallery, a former Methodist chapel at Les Augres, Trinity, Jersey, which Sir Francis was in the process of converting into a studio and art gallery when he died.