Graham's film roles include Scrum in Pirates of the Caribbean: On Stranger Tides (2011) and Pirates of the Caribbean: Dead Men Tell No Tales (2017), Anthony Provenzano in The Irishman (2019), Andy Jones in Boiling Point (2021) and its sequel series of the same name (2023), and Patrick Mulligan in Venom: Let There Be Carnage (2021) and its sequel Venom: The Last Dance (2024).

[1] He had a Swedish grandmother and Jamaican grandfather, and has discussed his experience being a light-skinned multiracial person as he has brothers who have much darker skin.

[1] Graham has often portrayed characters from different parts of Britain, Ireland, and America, receiving praise for his accent work.

He appeared in the music videos for "I Remember" by Deadmau5 and Kaskade,[9] "Fluorescent Adolescent" and "When the Sun Goes Down" by Arctic Monkeys, "Unlovable" by Babybird (directed by Johnny Depp), and Gazelle's single "Finger on the Trigger".

In 2021, Graham starred alongside Walters in the film Boiling Point, directed by his Band of Brothers co-star Philip Barantini.

[18][19] In October 2022, it was announced that Graham would reprise his role in a BBC One series airing in 2023 as a sequel to the film, which was also called Boiling Point.

[20][21] Graham began dating actress and producer Hannah Walters after they met while training as actors at Rose Bruford College, and they were married on 6 June 2008.

[24] Graham was appointed Officer of the Order of the British Empire (OBE) in the 2023 New Year Honours for services to drama, which he dedicated to his mother, who died in 2022.