[1] His father died in 1920 (during the Irish War of Independence), and the family moved to Birmingham, England, where he attended King Edward's School.

[1] World War II began while Alexander was competing in the 8th Chess Olympiad in Buenos Aires, Argentina, prompting him and the rest of the English team to abandon the competition and return to the UK.

In mid-1946, Alexander joined GCHQ (under the control of the Foreign Office), which was the post-war successor organisation to the Government Code and Cypher School (GC&CS) at Bletchley Park.

[4] MI5's Peter Wright, in his 1987 best-selling book Spycatcher: The Candid Autobiography of a Senior Intelligence Officer, wrote about Alexander's assistance to MI5 in the ongoing Venona project, as well as other important mutual cooperation between the two organizations, which broke down previous barriers to progress.

At the 1939 Olympiad in Buenos Aires, Argentina, Alexander had to leave part-way through the event, along with the rest of the English team, because of the declaration of World War II, since he was required at home for codebreaking duties.

Alexander's opportunities to appear abroad were limited as he was not allowed to play chess in the Soviet bloc because of his secret work in cryptography.

[9] Many top players peak in their late twenties and early thirties, but for Alexander this stretch coincided with World War II, when high-level competitive opportunities were unavailable.

Alexander is portrayed by actor Matthew Goode in the 2014 film The Imitation Game, which depicts the British attempts to crack the Enigma machine at Bletchley Park.