An apprenticed lithographic draughtsman, he was introduced by his brother to the lectures of Frederick Denison Maurice at the Hall of Association, 34 Castle Street East, London, in 1853 and the summer of 1854. When the Working Men's College was formed in 1854, he attended John Ruskin’s first drawing classes.
He succeeded Ruskin as a Drawing Master at the College, and taught at other London establishments. During the 1850s and 1860s Cooke was influenced by Herbert Spencer, and became a student of Pestalozzi, developing an enthusiasm for the Pestalozzian and Froebellian methods in which he became an influential interpreter. With Thomas Ablett, Alexander Bain, and psychologist James Sully, he furthered art education thinking.
Sully and Cooke were a particular influence on each other.
He served on the Council of the Education Society (founded 1875) which later became Society for the Development of the Science of Education. In 1904 he sat on the Committee of the Third International Congress for the Development of Drawing and Art Teaching.
Vanessa Bell began her art education under the tutelage of Cooke.
