[2] Cura's first acting role came at age nine, as a supernumerary in a production of La Forza del Destino at the Opéra de Marseille, France.

He made his West End debut playing Angel in the original cast of Jennifer Saunders' musical Viva Forever at the Piccadilly Theatre in London, UK.

Cura's directorial debut, Creditors, world-premiered at the Nordic International Film Festival in New York City on 31 October 2015.

[16] In 2016, Cura was cast as a series regular in ITV/Netflix crime noir drama Marcella penned by The Bridge writer Hans Rosenfeldt.

[19] In 2017, he was cast in Simon West's action/comedy feature film Gun Shy opposite Antonio Banderas and Olga Kurylenko.

[20][21][22] Also in 2017, Cura was cast as CIA operative Philip Shafer in French historical war movie 15 minutes de guerre (renamed L'Intervention), directed by Fred Grivois.

In 2019, he was cast in Nicholas Wright's stage play 8 Hotels directed by Richard Eyre, world-premiering at the Chichester Festival Theatre, playing the lead role of José Ferrer opposite Tory Kittles, Emma Paetz, and Pandora Colin, opening 7 August of that year to excellent reviews: "Joe, played masterfully by Ben Cura, is wonderful as the philanderer who can accept his wife's adultery but not her lover's flaunting of it";[23] "Jose Ferrer [...] Ben Cura, who captures him very well, has a wonderful mutually mistrustful good-pals-act with the impressive Kittles";[24] "Ben Cura is excellent as Ferrer [...] with charisma to spare";[25] "Ben Cura plays José Ferrer as a much disappointed jobbing actor [...] playing Iago for peanuts opposite the better paid Robeson [...] This Ferrer becomes increasingly jealous of Robeson and is convinced that his wife, Uta Hagen [...] is having an affair with the charismatic Robeson (she is), which fills him with an angry cynicism that he can barely control with his erudite and scathing humour that cannot disguise his underlying lack of confidence.

[31] In 2022, Cura made his animation debut voicing Rayan in Tad, the Lost Explorer and the Emerald Tablet while guest starring in HBO Max and Hulu Japan's season 2 of The Head as Liam Ruddock, and starring in BFI and BBC short film My Eyes Are Up Here co-produced by his company W.I.P.

[34] Also that year, he appeared in Queen Charlotte: A Bridgerton Story produced by Shondaland and premiering on Netflix, in the recurring role of Prince Augustus.