Despite his heavy scoring at first-class level, Simpson was yet to hit a Test century when he arrived with his team in England in 1964. After making a slow start to the tour and not passing 31 in his first four innings, Simpson struck form after the first week of May. He passed 50 in seven consecutive innings, making 125 against Somerset, 138 and 55 against Surrey, 57 against Glamorgan, 95 against Cambridge University, and 105 and 52—both not out—in a nine-wicket win over the MCC. He augmented this with 4/48 against Surrey.