The youngest of five children, whose physician father was an amateur flutist and whose mother was an accomplished pianist, Eric began study on the violin at age six. Later on he took up the viola. He showed no serious interest in composing until age 20 when he entered the Royal Academy of Music, where he studied viola with Lionel Tertis and composition with Frederick Corder. In the period between 1908 and 1909, he wrote his first vocal works: Four old English Songs and Stonecracker John. In 1910 he began playing the viola in the Beecham Symphony Orchestra and shortly afterward got a similar post in the Queen's Hall Orchestra, under Sir Henry Wood. He turned out his first orchestral work, the Miniature Suite, in 1911. Two years later, Coates married 18-year-old Phyllis Black, who would write lyrics for him and be of immense help to him throughout his career. Because of a progressive neuritis in his left hand and arm, Coates was exempt from military service during the war years. By 1919, however, the condition forced him to give up his first-chair viola post in the Queen's Hall Orchestra.
In 1927, Coates composed his orchestral suite Four Ways, which achieved considerable popularity. Perhaps his greatest success, though, came with the 1933 London Suite, which contained a section called "Knightsbridge," a march that took on a life apart from the suite when it was used to introduce the BBC radio program In Town Tonight, which became familiar to virtually every British listener during its 27-year run.
When his wife began working for the Red Cross in 1940, Coates was moved to write Calling All Workers, whose theme was subsequently used by the BBC for another radio show, Music While You Work. The orchestral suites Four Centuries (1942) and Three Elizabeths (1944) merely solidified his position now as the composer of the most familiar British music of all time.
In the postwar years, Coates continued to turn out popular scores, like Music Everywhere (1949). The composer continued to be active as a conductor in his last years, taking up the baton at one notable Promenade concert in August 1956, after Sir Malcolm Sargent had led the orchestra in a Tchaikovsky work. The 70-year-old Coates led the ensemble in his Four Centuries Suite and drew an enthusiastic response from the audience. Coates suffered a stroke and died on December 23, 1957.