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-arm 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 married wife Dawn in October 1973 and has two daughters.

Underwood was appointed an MBE in the 1981 New Year Honours for his services to cricket.

He scored his first and only first-class century (111) at the age of 39, in his 591st first-class match in July 1984. It was played at Hastings, a favourite bowling haunt for Underwood who, having gone in to bat as nightwatchman, finally reached the hundred mark in his 618th first-class innings. The cricket writer Colin Bateman noted, “there was no more popular century that summer”.

Underwood retired from cricket in 1987, at the age of 42, having taken 2,465 wickets at a little over 20 apiece.

In 1997, he became patron of the Primary Club, and in 2008 it was announced that he would serve as President of MCC for the following year.

In a Wisden article in 2004, he was selected as a member of England’s greatest post-war XI.

Underwood was appointed an Honorary Fellow of Canterbury Christ Church University at a ceremony held at Canterbury Cathedral on 30 January 2009.