Allan was a noted numismatist and produced the first systematic study of the coins the Gupta Empire, which remains a standard reference today.
His father, John Gray Allan, was the local schoolmaster.
After studying at the universities of Edinburgh and Leipzig, Allan took up a position at the British Museum in 1907, eventually becoming the Keeper of the Department of Coins and Medals in 1931.
[3][4] He was elected a Fellow of the British Academy in 1941, and was made a Companion of the Order of the Bath (C.B.)
Allan wrote numerous books, articles, reviews and notices, many of which were published in the British Museum Quarterly, History of the Berwickshire Naturalists' Club, the Journal of Hellenic Studies, the Journal of the Royal Asiatic Society, the Numismatic Chronicle and the Numismatic Supplement to the Journal of the Asiatic Society of Bengal and the Museums Journal.