Thornton was born in Rawalpindi, then in India, the son of Edward Parry Thornton C.B. and Louisa Chicheliana Plowden. Edward Thornton was the grandson of Samuel Thornton, former Governor of the Bank of England and was Commissioner of Rawalpindi from 1849 to 1858 under Lord Lawrence, and Judicial Commissioner for the Punjab from 1858 to 1862.
Between 1867 and 1869, Alfred attended Harrow School. A younger brother, George Walter Thornton, also attended Harrow (from 1869 to 1871). He died at Avranches in Normandy on 2 May 1873.
By profession, he was a banker. He was awarded the C.B. in 1860 in recognition of his services. In March 1870, along with Bowen, he was invited to play for the English XI in a match arranged by C. West. Alcock against a side representing Scotland.
This was the first of a series of matches played over the next two years, before the first official football international in November 1872.
There was no score in the match until 75 minutes had elapsed, when the English goalkeeper moved out of goal to play upfield. The Scots took advantage of the exposed goal when Robert Crawford scored with a shot from distance:. the game progressed until within a quarter of an hour of the time determined for the cessation of play, when the English rashly removing their goalkeeper paid the penalty by witnessing the reduction of their fortress to a long shot by R.E. Crawford.
England fought back to score through Alfred Baker to salvage a draw a minute from the end of the game. On 14 October 1871, he played for Harrow Chequers against the Wanderers.
The teams played out a 0–0 draw. The Morning Post mentioned Thornton as "conspicuous for excellent play".
Three days later, Thornton played for the Wanderers in a 1–0 victory over the Civil Service.
On leaving school, Thornton became a banker progressing to manager of the Old Bank and Brewery at Windsor. The bank and brewery were owned by Nevile, Reid & Company and was originally founded as Ramsbottom & Baverstock in 1780. In 1914, the bank was acquired by Barclays Bank.
The brewery was acquired by Noakes & Company of Bermondsey, London in 1918, eventually becoming part of the Courage Brewery.
In the 1881 census, he was shown as living at 51 Thames Street, Clewer, Berkshire. His occupation was "banker".
Thornton was also a Justice of the Peace for the County of Berkshire. He died on 31 March 1906, aged 53.
In his final year at Harrow, he was a member of the school football team Thornton was a member of the Wanderers club, to whom he was probably introduced by East. East. Bowen, a master at Harrow School. As well as being a member of the Wanderers, Thornton played for the Harrow Chequers.
