Son of a yeoman farmer of Kingsbridge, South Devon, Francis Coaker studied medicine at the London Hospital. After holding resident appointments there he settled in practice at Bromsgrove in 1897. There he combined a large general practice with the post of surgeon to the Bromsgrove Cottage Hospital, which he expanded and modernised. Coaker was Medical Officer of Health for Bromsgrove Rural District Council from 1902 to 1946, he was Medical Officer to the guardians for many years, surgeon to the Worcestershire Mental Hospital, and a governor and later chairman of King Edward VII Sanatorium, Knightwick, near Worcester. In 1917 he was elected a member of the Worcestershire County Council and took an active part in the work of its committees, becoming chairman of the health committee. Coaker played a large part in securing the adoption of the BMA salary scale for public health medical officers in Worcestershire in the mid-twenties before any national scales were in operation. He often acted as arbitrator in disputes. He was chairman of the Bromsgrove Division of the BMA 1921-22, and of the Worcester and Bromsgrove Division in 1935-36, and president of the Worcestershire and Herefordshire Branch in 1937-38. During the second world war he was acting assistant secretary of the Worcester and Bromsgrove Division. Coaker became the "father" of the medical profession in Bromsgrove; he lived at Sunnymead, New Road until his retirement to Hele House, Dulverton, Somerset, where he died on 14 January 1955 aged 83. His wife, Diana Augusta Coaker, died on 28 March 1960 at Cliffden, Teignmouth, Devon, aged 79.