He played for the Cambridge cricket team in both 1952 and 1953, winning a Blue in both years for appearing in the University Match against Oxford.
He also appeared in a trial match for the West Indies tour to England that summer, sharing a stand of 134 with Wes Hall.
However Frank Worrell declined the position because he was studying for a degree in economics at Manchester University, and the other senior players Everton Weekes and Clyde Walcott were apparently not considered suitable.
Thus Alexander was offered the job and, as his Telegraph obituarist writes "through patience, skill and encouragement... succeeded in forging the array of talent in the West Indies side into a coherent and successful team.
For the first time since World War II they had to manage without any of the "three Ws" who had been the core of their batting: Worrell, Weekes and Walcott.
On the only occasion that they were in difficulties, against the leg-spin of Subhash Gupte in the second Test, Alexander scored 70 to save the day.
[2] The following winter, West Indies lost by one Test to nil against England, with four matches drawn, under Alexander's captaincy.
The West Indies lost heavily in the second Test in Trinidad, and the crowd rioted when they collapsed in their first innings.
According to his obituarist: "The dismissed captain had taken over a side in total disarray and laid the foundations for future triumphs.
His century at Sydney was an important factor in enabling West Indies to win, and was the only one of his first-class career.