Curzon made his first-class debut for Nottinghamshire against Northamptonshire in the 1978 County Championship. During the same season Curzon also made his one-day debut against Yorkshire. Curzon represented the club in seventeen first-class matches, the last of which came against Yorkshire in 1980. Curzon's last one-day game for Nottinghamshire came against Northamptonshire in the Quarter-Final of the 1980 Benson and Hedges Cup. This was also to be the last one-day game of Curzon's career. At the end of the 1980 season Curzon left Nottinghamshire.
Curzon played a single first-class match for Hampshire in 1981 against the touring Sri Lankans. This was his only appearance for Hampshire.