On-screen, Graham appeared in two episodes of the first series of Doctor Who as an actor, but became much better known as the unemotional, harsh voice of the Daleks.

Graham was born in London on 11 July 1925. His sister had married a G.I. and had moved to the United States, and his uncle had run away there, and so he became an actor after leaving his Orthodox Jewish household. He trained in New York City, at the Neighborhood Playhouse School of the Theatre with Sanford Meisner, following service in the Royal Air Force as a radar mechanic.

Graham returned to England and began his theatre career, his breakout role being as Givola in The Resistible Rise of Arturo Ui, alongside Leonard Rossiter. A friend of his, actor Christopher Benjamin, recommended the role to him. He was then recommended by director Michael Blakemore to audition for Laurence Olivier’s theatre company, eventually appearing alongside him in Saturday Sunday Monday, using an Italian accent.

While playing characters in the TV series Private Investigator in 1958, Graham met writer and producer Gerry Anderson, who was planning his first puppet productions. Graham said that he could pull off accents well, which led to his first voiceover role in Four Feather Falls, as Grandpa Twink, who he based on Walter Brennan. He would subsequently voice Dr. Beaker, Zarin and Mitch the Monkey in Supercar, Mat Matic and Lieutenant Ninety in Fireball XL5 and various guest characters in Stingray. Graham would also play Johnny in Crossroads to Crime, a live-action film Anderson directed.

In 1963, he became the voice of the Daleks in Doctor Who, alongside Peter Hawkins, who devised the way they spoke. He believed Hawkins would always play superior and higher-pitched Daleks, while he voiced with a lower-pitch. He voiced the Daleks in all four of their major First Doctor era appearances, as well as two 1960s feature films: Dr. Who and the Daleks and Daleks’ Invasion Earth 2150 A.D., departing due to other commitments, although he and Hawkins would remain lifelong friends. Graham also voiced the Mechonoids and played the onscreen role of Charlie in The Gunfighters. He returned to his role as the voice of the Daleks in 2023, when he recorded new lines for that year’s official colourised recut of the 1963 serial The Daleks for the show’s 60th anniversary.

In 1965, Graham became the voices of Gordon Tracy, Brains, Aloysius Parker and Kyrano in Thunderbirds, as well as its film sequels: Thunderbirds Are Go and Thunderbird 6. He did not believe Brains had a stutter, claiming that he was instead trying to find the words to explain his latest ideas excitedly. He based the voice of Parker on a waiter at the King’s Arms pub in Cookham, and he and Ray Barrett shared many of the guest villains. Although he was not highly paid for production, the many repeats earned him a lot more, and Parker became Anderson’s favourite voice.

Between 1975 and 1977, Graham was part of the Radio Drama Company. In 1979, he played Professor Kerensky in the Doctor Who story City of Death. He, later, played the role of Big Brother in the “1984” television Super Bowl advert to introduce the Apple Macintosh computer before reuniting with Hawkins and his wife, Rosemary Miller, to provide voices together in the English dub of German animated film Stowaways on the Ark. In 2004, Graham became the voice of Grandpa Pig in Peppa Pig, having known creator Mark Baker from when he was younger. The following year he played Albert Einstein in a Horizon docudrama, for which he was very proud that the BBC would select him to play the lead role.

In 2009, Graham began playing Edward Elgar in Stirring the Spirit, for which he thoroughly researched the composer, and would reprise the role many times over the next decade. From 2015 to 2020, he reprised his role as Parker in Thunderbirds Are Go, a reboot of the original series. Although Kayvan Novak took over as Brains, Graham had wanted to reprise that role as well. Most of his dialogue was recorded with Rosamund Pike, who played Lady Penelope Creighton-Ward.

In April 2021, Graham announced his retirement from his Thunderbirds characters. In December, actor George Layton, a long-time friend of Graham’s, announced on Twitter that Graham had suffered a stroke six months earlier and was unable to leave his home in London. However, Layton stated that Graham was recovering by performing voice-overs, and he has since conducted interviews from his home.

Graham died on 20 September 2024, at the age of 99.