Denness was born in Bellshill, North Lanarkshire, Scotland. His father was employed by W.D. & H.O. Wills, a tobacco importer and cigarette manufacturer and part of Imperial Tobacco.

After his family moved to Ayr, he was educated at Ayr Academy, where he played rugby with Ian Ure and Ian McLauchlan and played for Ayr Cricket Club at Cambusdoon, where he was coached by former Sussex player Charles Oakes. Denness was selected to play cricket for Scotland against Ireland in 1959 while still at school. Former Kent bowler Jimmy Allan was also in the Scotland team, and he suggested Denness's name to his former county. E. W. Swanton also met Denness in Ayr and put in a good word, and Les Ames invited Denness to a trial in 1961.

Denness made his first-class debut for Kent against Essex in July 1962, but was dismissed by Jim Laker twice on a turning pitch for 0 and 3. But he quickly established himself in the team, scoring over 1,000 runs in the 1963 season. From 1964 played as an opening batsman in partnership with Brian Luckhurst.

He became a tall, stylish right-handed batsman. He received his county cap in 1965 and Kent won the County Championship in 1970 for the first time since 1913. He succeeded Colin Cowdrey as Kent captain at the beginning of the 1972 cricket season, having often substituted for Cowdrey when he was on Test duty. Under his captaincy, the club won the John Player League three times (1972, 1973, 1976), the Benson & Hedges Cup twice (1973, 1976), and the Gillette Cup once (in 1974; also his benefit season). Denness was a Wisden Cricketer of the Year in 1975. After 5 years as captain, the club voted to replace him as captain by Asif Iqbal at the end of the 1976 season.

After being dismissed as captain at Kent, he moved to Essex in 1977, helping the club to win the County Championship and Benson & Hedges Cup in 1979. He retired after the 1980 English cricket season.

In all, he made 501 appearances in first-class cricket and 232 more in one day matches. He scored over 30,000 domestic runs in all, including 33 first class hundreds and a best of 195, and six one-day centuries with a top score of 188 not out. He also took two wickets with his occasional bowling. He scored over 1,000 first-class runs in 14 English cricket seasons.

After he retired as a player at the end of the 1980 English cricket season Denness became 2nd XI captain at Essex and also worked as a coach. Outside cricket he had jobs in finance, insurance and public relations.

Denness played for England in 28 Tests and was captain on 19 occasions, winning six, losing five and drawing eight matches. He made his Test debut in the final test against New Zealand at The Oval in 1969. After