The Gun Control Network said allowing children to use powerful weapons, such as shotguns, is "absurd" and warned that weapon security cannot be guaranteed with youngsters.
But the British Association of Shooting and Conservation says teaching children how to enjoy the benefits of responsible shooting is to be encouraged.
At the end of March, 33 children aged under 18 in Lincolnshire held certificates granting them permission to use shotguns or firearms, according to Home Office data.
They were among 13,601 people in the area permitted to use the weapons.
There is no minimum age to hold a shotgun certificate in England and Wales, but a child must be over 14 to have a firearm certificate.
The figures show 33 shotgun and five firearm certificates, granted by Lincolnshire Police, are held by youngsters aged between 14 and 17 – some of whom could hold both types.
The law restricts children to the use of firearms for animal slaughter, sport, competition, target shooting and the shooting of vermin.
They cannot purchase their own weapons or ammunition but are entitled to possess some firearms from the age of 14.
And certificate holders under 15 are allowed to borrow shotguns for use under adult supervision but cannot be given a shotgun of their own until they reach 15.
Across England and Wales, 2,084 certificates were held by under-18s as of the end of March, with the youngest holder of a shotgun licence believed to be just seven.
That represents a drop from 2,770 in March 2020, while in Lincolnshire, the number of children holding certificates also fell from 49 over the same period.
Peter Squires, from the UK Gun Control Network, said: "The fact that children can be licensees is a ridiculous anomaly, given that children could never be legally responsible in their own right for the safety and security of the weapon.
"GCN believe firmly that the privilege to own and use a firearm should be tied very closely to the responsibility for its use and security. This cannot be assured with children."
For anyone to obtain a firearm or shotgun certificate, the chief officer of their local police force must be satisfied that they have good reason to have a weapon, that they are fit to be entrusted with it and that public safety or peace would not be endangered.
Martin Parker, of the BASC, said current legislation benefits those in training for Olympic and Commonwealth shooting disciplines and those being taught pest control techniques.
He added: "Encouraging younger people to enjoy the benefits of responsible shooting, while teaching the principles of safety and self-discipline, is to be encouraged."
A Home Office spokesperson said the UK had some of the toughest gun laws in the world, with firearm possession subject to stringent controls.
He added: “There are strict controls on young certificate holders who must be thoroughly vetted by the police.’’