Underwood was born in Bromley Maternity Hospital, the second son of Leslie Frank Underwood and Evelyn Annie Wells. His early days were spent watching his father, a right-handed medium pace bowler, play for Farnborough Cricket Club, where older brother Keith also played. Underwood was educated at Beckenham and Penge Grammar School for Boys and in 1961 he took all ten wickets for the school's First XI, of which his brother was the captain, against Bromley Grammar School.

Underwood played county cricket for Kent, making his first-class debut against Yorkshire aged 17 in 1963. He became the youngest player to take 100 County Championship wickets in a debut season. He went on to take 100 wickets in a season a further nine times. His batting was less accomplished, averaging barely over ten runs per innings in 676 matches.

Underwood took the last four Australian wickets in 27 balls in the final half an hour at the end of the fifth Test in 1968, after a heavy thunderstorm on the fifth day had all but ended the match, to square an Ashes series that Australia were winning 1–0. He was named in 1969 as one of the Wisden Cricketers of the Year. Underwood also toured Australia in 1970–71, dismissing Terry Jenner to win the seventh Test at Sydney, and regain the Ashes.

According to the retrospective ICC Test bowler rankings, Underwood was ranked number 1 in the world from September 1969 to August 1973. He reached a peak rating of 907 after his 12-wicket haul against New Zealand in the 1971 series.

Underwood was one of five England cricketers (the others being Alan Knott, Dennis Amiss, Bob Woolmer and Tony Greig), to feature in Kerry Packer's World Series Cricket in the late 1970s.

He also went on the rebel tour South Africa in 1981–82, bringing his England career to an end as it was in defiance of the sporting ban against the apartheid state. For this he and the other rebels were banned from international cricket for three years.