Dandy was educated at Preston Grammar School and after that at Downing College, Cambridge, where he took his B.A.
In 1925, he was appointed as an assistant to John Hutchinson at Kew Gardens, who worked on a new Angiosperm classification.
On 11 July the same year, he was appointed Second class Assistant at the British Museum Department of Botany.
In 1936 he was promoted to First class Assistant, in 1946 to Principal Scientific Officer, and in 1956 he eventually became Keeper of Botany.
After his retirement, he kept active in the field of botany until he fell seriously ill, in July 1976.