Alexander Williams was born on 8 June 1910 in Herringston House, Dorchester, Dorset, England, the son of Captain B. C. W. Williams, a British Army officer, and Hon. Mrs Winifred Mary Williams, the elder daughter of the second Lord Addington. He was educated at Eton College before attending the Royal Military College, Sandhurst, from where he was commissioned as a second lieutenant into the King's Royal Rifle Corps (KRRC) on 28 August 1930. He was posted to the 2nd Battalion, KRRC, then serving in Tidworth, Wiltshire, before the battalion moved in 1932 to Northern Ireland. Promoted to lieutenant on 28 August 1933, the 2nd KRRC returned to England in 1935. Williams, along with the battalion, now commanded by Lieutenant Colonel Evelyn Barker, was sent to Palestine in 1936, following the outbreak of the Arab revolt, before again returning to England, in 1937, where it was converted into a motorised infantry battalion and became part of the Mobile Division (from April 1939 1st Armoured Division), under Major General Alan Brooke. In January 1939 Williams, who on 28 August 1938 was promoted to captain, was made adjutant to the 2nd KRRC, now commanded by Lieutenant Colonel Thomas Wilson after Barker was promoted to command a brigade.