Underwood was born in Bromley Maternity Hospital, the second son of Leslie Frank Underwood and Evelyn Annie Wells . His love for cricket was nurtured from a young age, watching his father-a right-arm medium pace bowler-and elder brother Keith play for Farnborough Cricket Club . Educated at Beckenham and Penge Grammar School for Boys, Underwood displayed prodigious talent early on. At just 16, he famously took all ten wickets for his school's first XI against Bromley Grammar School, with Keith as captain.

In 1963, aged only 17, Underwood made his first-class debut for Kent against Yorkshire. He quickly established himself as a force to be reckoned with, becoming the youngest player ever to take 100 County Championship wickets in a debut season. Over two decades, Underwood remained loyal to Kent, taking 100 wickets in a season no fewer than ten times during his illustrious career. Though his batting was less distinguished, averaging barely over ten runs per innings, he achieved a remarkable milestone by scoring his only first-class century (111) in 1984, playing as a nightwatchman against Sussex at the age of 39 .