Esmonde was born on 1 March 1909 in Thurgoland, Yorkshire, near Barnsley, where his Irish Catholic father, Dr John Joseph Esmonde (1862–1915), was in temporary general practice. Esmonde had three elder half-brothers and three half-sisters from his father's first marriage to Rose McGuinness. His brothers were: Sir John Esmonde, 14th Baronet, who served in the First World War; Second Lieutenant Geoffrey Esmonde (1897–1916), who was killed in action in the First World War serving with the 26th Tyneside Irish Battalion of the Northumberland Fusiliers; and Sir Anthony Esmonde, 15th Baronet. After the death of his first wife John Esmonde elder married Eily O'Sullivan, who bore him five sons and one daughter: Owen, Donal, John Witham, Eugene and his twin James, Carmel and Patrick. Thomas Esmonde, who was awarded the Victoria Cross in the Crimean War, was a great-uncle.