Stewart Jackson has written to the council's chief executive Gillian Beasley, expressing concerns over the 12A rating given to the film, which has attracted controversy because of its violent content and dark themes.
At present children as young as 12 years of age are able to view the film on their own and younger children can see it if accompanied by an adult.
In his letter, Mr Jackson reminded her that the council can use its discretion under current legislation to reclassify the rating given by the British Board of Film Classification (BBFC).
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He said: "I am not a spoilsport and I have seen this film but I sincerely believe that it is not suitable for children. The violence is gratuitous and the dark themes inappropriate for children's viewing.
"I believe that the BBFC have made an error of judgement and I have written to the city council to amend the recommended classification."
Dubbed sensational and the biggest baddest movie of the year, The Dark Knight set a box office record for best opening weekend ever when it hit screens in the US.
The sequel took $158.3 million (£77.7 million) in North America, beating the record set last year by blockbuster Spider-Man 3, which took $151.1 million (£75.5 million).
The film sees Gotham city shaken by the rise of a new criminal named The Joker. With The Joker terrorising the citizens of Gotham, Batman teams up with lieutenant Gordon and District Attorney Harvey Dent to help bring this madman to justice.
But Batman has to reach into his dark side to catch the maniac before he tears Gotham apart.
Richard Kendall (34) of Botolph Green, Orton Longueville said: "I thought that the visuals were well worked to cover some of the violence in the film.
"However, I did think that perhaps the content of the film was a bit disturbing. The Joker is portrayed as a crazy man who uses knives which could be a bit much for young people.
"The subject matter was perhaps a bit deep and advanced for a child to understand."
A spokesman for the city council said that while the council is responsible for licensing cinemas, ensuring that the films being shown there have been certified and they are adhering to age restrictions, they would not attempt to reclassify a film, which had been classified by the BBFC, the experts in this field.
However, they may classify a film which has been independently made and is to be shown locally.
He added: "While we have received no complaints about the classification of Batman, we suggest anybody who wants to should direct their complaint to the BBFC."
Directed by Christopher Nolan, the film cost $185 million (£92.5 million) to make and stars Christian Bale as the Caped Crusader, the late actor Heath Ledger, who plays the Joker and Michael Caine as Alfred, Bruce Wayne's butler.
The full article contains 547 words and appears in Peterborough ET newspaper.