From Anthony Hopkins in Oliver Stone’s epic biopic to Frank Langella in Frost/Nixon and John Cusack in The Butler, cinema clearly has a fascination with the disgraced US president Richard Nixon – perhaps because his unlovely shapelessness makes him easy to imitate. The charismatic Elvis Presley has proved harder to depict on film, but director Liza Johnson’s shallow yet engaging comedy uses two creditable impersonations to tell the story behind the most requested photo in the US National Archives.

Told from the POV of hangers-on in both camps, Presley (Michael Shannon) is introduced as a weary star, disenchanted with the music business, and seeking to address his feelings of unhappiness by offering his services as an undercover agent to President Nixon (Kevin Spacey). Portrayed as a square with a distaste for Presley’s showmanship, Nixon initially refuses to meet him, but ends up finding common ground when the singer arrives at his door.

Elvis & Nixon gets considerable comedic mileage from the notion that both men understand that they have a carefully constructed public image to protect, one that they each fear falling short of. Spacey is note-perfect in his impersonation of Nixon, but Shannon wisely doesn’t attempt the same level of physical precision, instead offering a manic and somewhat haunted version of the star.

Johnson pulled off an accomplished Alice Munro adaptation with her 2013 drama Hateship Loveship, and brings some of the same offbeat sensitivities to a more cartoonish story here. The script, co-written by Princess Bride star Cary Elwes, may not have a great deal to say about either celebrity or politics but, as an extended sketch about the meeting of two remarkable figures, Elvis & Nixon manages to capture why the public retain such curiosity for these influential, eccentric men.

General release from Fri 24 Jun.