Somes was born in Horsley, Gloucestershire, England. In 1934, he was awarded the first scholarship given to a male by the Royal Ballet (then known as the Vic-Wells Ballet). In 1938, he and Fonteyn created the principal rôles in the Frederick Ashton/Constant Lambert ballet Horoscope, after which he was described as "potentially the finest British male dancer of the half century". He originated rôles in 24 ballets choreographed for the company by Ashton, and was the lead male dancer for the company from 1951 until the arrival of Rudolf Nureyev in 1962. From then on, Somes appeared in character rôles, most notably as Lord Capulet in Romeo and Juliet. Somes was assistant director of the company under Ashton from 1963-70.
Somes appeared on The Ed Sullivan Show in 1954, and in television versions of Swan Lake (1954), The Sleeping Beauty (1955) and The Nutcracker (1958), as well as a film version of Prokofiev's Romeo and Juliet (1966). All three productions starred Margot Fonteyn.
In 1959, Somes was named a Commander of the Order of the British Empire (CBE). He was married to fellow ballet dancer Dame Antoinette Sibley, but they eventually divorced. He later married ballet dancer Wendy Ellis. He died of a brain tumour in London in 1994.