At the age of 13, having participated in an opening partnership of 467 with Henry Betts in a house game, Simpson was selected for the High School first team.
He first gave notice of his abilities at a higher level scoring 134 not out for Nottinghamshire County Cricket Club against the RAF at Trent Bridge in 1940.
During the war he served as a pilot with the RAF but also took the opportunity to play cricket for the RAF alongside the likes of Wally Hammond and Bill Edrich, for the Europeans in India alongside Joe Hardstaff junior and Denis Compton and occasional games for Notts.
Following the war Simpson made an immediate impression on the game, and was picked for the 1948–49 tour of South Africa on which he played his first Test, without success.
[3] This innings was the finest of his career, first adding 131 with Hutton and making 64 out of a stand of 74 for the last wicket, to put England 103 runs ahead, and gave them their first victory against Australia since 1938.