Slow left-armer Underwood took 297 wickets in 86 Tests between 1966 and 1982, the most by any England spinner.
He claimed 2,465 wickets in 676 first-class matches overall, representing only Kent, the county of his birth, in a stellar 24-year domestic career.
Underwood was appointed an MBE in 1981 and was president of the Marylebone Cricket Club in 2009.
He also took 32 wickets in 26 one-day internationals and would have represented England more but for joining World Series Cricket in 1977 and the rebel tour of South Africa in 1981-82.
Nicknamed ‘Deadly’, Underwood was one of 55 inaugural members inducted into the International Cricket Council Hall of Fame when it launched in 2009.
Kent Cricket chair Simon Philip said the club is “in mourning following the passing of one of its greatest ever players”.
He added: “Derek was an outstanding contributor to both Kent and England, winning trophies for club and country and etching his name in the history books forevermore.”
Known for his high level of accuracy, Underwood would often bowl much quicker than most spinners but was also able to deceive batters with variations of pace and length.
He was particularly challenging to face on uncovered pitches that had been affected by rain, his faster pace helping to skid the ball on to batters quickly, while also able to extract turn on surfaces starting to dry out.
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“Watching Derek weave his unique magic on a wet wicket was a privilege for all who were able to witness it,” added Philip.
“His induction into the ICC Hall of Fame shows the esteem in which he was held in world cricket.
“An advocate for growing our game worldwide whilst protecting our sport’s rich heritage, Derek also made substantial contributions off the field as well as on it, and he will be sorely missed by everyone at Kent Cricket.”
Underwood is sixth on England’s Test wicket-takers list, having taken 42 more scalps than the next spinner and seventh overall, Graeme Swann.
Born in Bromley in 1945, Underwood made his Kent debut in 1963 aged just 17 before making his Test debut against West Indies three years later.
He helped England to a famous win over Australia in the fifth Test of the 1968 Ashes at The Oval, taking the last four wickets to fall in just 27 balls during a frantic finale after the crowd had helped dry the ground following a rain delay.
Underwood formed a productive partnership for England and Kent with wicketkeeper Alan Knott. Both players joined Kerry Packer’s breakaway World Series Cricket in 1977, pausing their international careers until after the competition ended in 1979.
Underwood’s England career came to an end in 1982 when he joined a team led by Graham Gooch in touring South Africa, defying the sporting boycott of the country during the Apartheid.
He scored his first and only first-class century against Sussex in 1984 at the age of 39, having gone in to bat as a nightwatchman.
Underwood retired from cricket in 1987, having won three County Championships, two One-Day Cups, three National Leagues and three Benson & Hedges Cups for Kent.
England and Wales Cricket Board chair Richard Thompson said: “It is always a sad day when a great of the English game passes away.
“Derek Underwood will be remembered as one of the finest spin bowlers this country has ever produced, and his remarkable record is testament to his enduring skill.
“Our thoughts are with Derek’s friends and family, everyone at Kent, and everyone who knew and loved him.”
