Citing figures released under the Freedom of Information Act, The Sun reported that 13 children under the age of 10 were granted certificates between 2008 and 2010.
The data was obtained from 51 forces in the country. A total of 7,071 licences were awarded to people under 18.
The seven-year-old was given the licence by Gloucestershire police, while West Mercia police approved one for an eight-year-old.
The eight-year-old was given a licence for clay pigeon shooting while being supervised by his dad, police said.
Police chiefs have now asked for the "absolute minimum age" for shooting with firearms to be 10.
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