He was born in Dublin in 1889 the son of Thomas Alcock and his second wife, Agnes.
Thomas Alcock was born in Oxton, Nottinghamshire, and was a regular soldier. In 1881 he was serving at Shorncliffe Camp, Kent, where he was living in quarters with his first wife, Ellen (26, b. Glasgow) and their three children, Elizabeth E (4, b. Portsea, Hants), Thomas R (2, b. Portsmouth) and Charles (1, b. Shorncliffe).
Thomas later served in Dublin as his children by his second wife, Agnes, were born there. Agnes was also born in Ireland.
However, by 1901 at the age of 52 he was a night watchman and living at 5 Denman Street, Radford. He and Ellen (37) had four children at home; Alexander (12), Mary (8), Ellen Seymour (7, b. 25 August 1893) and Victoria Maud (3). A second son, Louis Josh Alcock (14) was working as a groom for William Henry Gray, a surgeon, of 68 West Gate, Mansfield.
Alexander enlisted in the army on 3 November 1902 and in 1911 was serving as a lance-corporal with the 2nd Battalion, Border Regiment, in Hampshire.
By 1911 Alexander's siblings Louis (24) and Ellen (17) were living with their half-brother, Charles Alexander Alcock (31) and his wife Edith (nee Drinkwater, m. 1905) at 42 Marcus Street, Lenton.
Ellen Seymour Alcock married Herbert Noah Pembleton on 14 March 1914. Her widowed half-brother, Charles, married Herbert Pembleton's widowed sister-in-law, Eliza Pembleton, in 1921 (previously married to George Albert Pembleton, served Sherwood Foresters, killed 1917).
The Register of Soldiers' Effects gives an extensive list of legatees to whom modest payments were made. All the legatees appear to be Alexander's brothers or sisters, some of whom were the children of his father's first marriage: Thomas and Charles (half-brothers), William, Bernard, John, Charles, and Mrs Victoria Fahey, Mrs Teresa Maud Bates, Mrs Ellen Seymour Pembleton, and the husband of Mrs Maddens.