Born the son of the Reverend H. G. Baker of Budleigh Salterton, Baker was educated at Christ's College, Christchurch and at Bedford School, and then attended the Royal Military College, Sandhurst where he passed out first in his class. He was commissioned to the unattached List of the Indian Army on 20 January 1909 and posted to the 31st Duke of Connaught's Own Lancers on 29 March 1910 and was promoted to lieutenant on 20 April 1911. Baker saw service in World War I. He was deployed to France on 13 March 1915 and became attached to the 34th Poona Horse on 31 May 1915. Promoted to temporary captain in the Cheshire Regiment on 21 September 1915 and to major in that regiment on 15 May 1916, he was promoted to the substantive rank of captain on 1 September 1915. Baker was promoted to acting lieutenant-colonel on appointment as acting commanding officer of the 1st battalion of the Cheshire Regiment on 22 August 1916 and awarded the DSO. He was also mentioned in despatches three times. He was promoted to brevet major on 1 January 1918 and to acting major in the Indian Army on 3 February 1918 while temporary second in command of the 31st Duke of Connaught's Own Lancers. He took part in the operations against the Marris between 18 February to 8 April 1918.
Between the wars
Baker took part in the Third Anglo-Afghan War in 1919 and was mentioned in despatches. Later in 1919 he was appointed an Instructor at the Cavalry School at Saugor before attending the Staff College, Quetta from 1921 to 1922. He became a General Staff Officer Grade 2, on the General Staff at Southern Command on 24 August 1922 shortly before the 31st Duke of Connaught's Own Lancers and 32nd Lancers were amalgamated in 1923 to form the 13th Duke of Connaught’s Own Lancers. He became a GSO2 with the Australian Military Forces on 1 January 1924 and was attached to the Department of the Chief of the General Staff in Australia. Promoted to the substantive rank of major on 20 January 1925, he was appointed Squadron commander with the 13th Duke of Connaught’s Own Lancers on 1 October 1928. He became a General Staff Officer 2nd grade at the Directorate of Staff Duties on 1 November 1929 and was promoted to brevet lieutenant-colonel on 1 July 1930. He transferred to Probyn's Horse on 30 July 1933 as second in command and attended the Senior Officers Course at Sheerness in 1934. Promoted to the substantive rank of lieutenant-colonel on 20 January 1935, he attended a course at the Imperial Defence College in 1936. He became commanding officer of Probyn's Horse on 1 November 1935 and took part in operations in Waziristan in 1936 and 1937. Baker was promoted to local temporary brigadier and given temporary command of the Kohat Brigade on 20 May 1936. He then reverted to local temporary colonel and was given temporary command of the Tochi column on 10 December 1936. He was appointed an Officer of the Order of the British Empire on 10 December 1937 for service in his role as commander officer of the 2nd Sialkot Cavalry Brigade during operations in Waziristan from 25 November 1936 to 16 January 1937. He was also mentioned in despatches for his service in Waziristan for the period 25 November 1936 to 16 January 1937. Promoted to colonel on 15 January 1938 with seniority from 1 July 1934, he became Commander of the Delhi Brigade Area on 15 January 1938.
He married Dorothy in 1924, third daughter of botanist John Henry Lace of the Imperial Forest Service. They had one son and one daughter. Baker died on 28 December 1964 in Devon, England.