Cursham made his County Cricket debut during the 1876 season, playing his first game for Nottinghamshire in a low-scoring victory against Yorkshire.
He, along with the rest of the Nottinghamshire team, failed to impress in a match in which only one player would reach double figures in each of the first three innings, himself scoring just three runs from the middle order.
Cursham, a right-handed batsman and a round-arm bowler, appeared extensively for Nottinghamshire during the 1877 and 1878 seasons, scoring a maiden career half-century against Middlesex in 1877.
He played regularly in the Derbyshire lower order, scoring a duck in his debut innings, though failing to break into the side as a bowler.
Three years after the end of his cricketing career, Cursham played two further games for the England national football team, a victory against Wales in which he scored his second and final international goal, and a defeat against Scotland.