The London-born star also voiced the evil Daleks in Doctor Who, and brought to life the Thunderbirds puppet characters aquanaut Gordon Tracy, scientist Brains and Lady Penelope's driver, Aloysius "Nosey" Parker, in the television series in which a secret organisation tried to save the world.
The son of Thunderbirds creator Gerry Anderson, the TV producer Jamie Anderson, said in a statement to the PA news agency he was "very sad to confirm that David has passed away at the grand old age of 99".
We're incredibly sad to confirm the passing of the legendary David Graham. The voice Parker, Gordon Tracy, Brains and so many more. David was always a wonderful friend to us here at Anderson Entertainment. We will miss you dearly, David. Our thoughts are with David's friends and… — Gerry Anderson (@GerryAndersonTV) pic.twitter.com/DB4HTawHiUSeptember 20, 2024
"Just a few weeks ago, I was with 2000 Anderson fans at a Gerry Anderson concert in Birmingham where we sang him happy birthday - such a joyous occasion," Anderson said.
"And now, just a few weeks later, he's left us. David was always kind and generous with his time and his talent. And what a talent.
"From the Daleks to Grandpa Pig and numerous voices for Anderson shows including Brains, Gordon Tracy and the iconic Parker. He will be sorely missed."
Graham returned as Parker for ITV's remake Thunderbirds Are Go, which ran between 2015 and 2020, but not for the live-action 2004 film which saw Ron Cook take on the role.
The original 1965 Thunderbirds was created by Gerry, who died in 2012, and his second wife, Sylvia, the voice of Lady Penelope, who died in 2016.
The official account of Anderson said on X: "David was always a wonderful friend to us here at Anderson Entertainment. We will miss you dearly, David. Our thoughts are with David's friends and family."
Graham played Grandpa Pig in children's show Peppa Pig, and also provided the voice for characters in Ben & Holly's Little Kingdom.
His in-person acting roles included Doctor Who, Coronation Street and Casualty.