Almost 600,000 people living in England and Wales have the right to carry guns, but police cannot say how many of them have criminal records.
Police forces across the country drew a blank when the Yorkshire Post asked them how many firearm and shotgun licence holders had been convicted of criminal offences.
A flaw in police recording systems means that checking each certificate one by one is the only way officers can find the number of gun-owners who have broken the law.
One police force, with more than 34,000 gun certificates on its books, admitted it would take almost four years to retrieve all the data.
Gun owners' convictions are likely to come under greater scrutiny in 2011 after an influential panel of MPs recommended that criminals who receive suspended jail terms should be stripped of any gun licences they hold.
The Commons Home Affairs Select Committee, which proposed the measure, described the country's gun laws as a "complex and confused" mess last month after conducting an inquiry into firearm licensing arrangements.
Calls for tighter restrictions on licences have grown louder since June, when a taxi driver with a criminal record went on a shooting spree in Cumbria, killing 12 people before turning a weapon on himself.
Derrick Bird, who owned his guns legally, was given a six-month suspended prison sentence 20 years ago for stealing decorating materials from his then employer.
He also had a drink-driving conviction and had been arrested over claims he "demanded payment with menaces" after a customer got out of his cab without pay- ing.
Bird, 52, was allowed to keep his shotgun certificate, which he obtained shortly before his 17th birthday, because neither of his convictions warranted an immediate custodial sentence to trigger an automatic ban.
In its most recent publication on gun licence data, the Home Office revealed that 138,728 firearm and 574,946 shotgun certificates were on issue in England and Wales at the end of March 2009, covering a total of more than 1.8 million guns.
In Yorkshire there were 59,300 gun certificates relating to 144,306 weapons, of which about 40 per cent belonged to licence holders in the north of the region, where shotgun use is high in rural areas.
More than 24,000 certificates were on issue in North Yorkshire, about 13,000 in West Yorkshire, about 12,500 in the Humberside police force area and less than 10,000 in South Yorkshire.
Only one police force in England and Wales – City of London Police, which issues the fewest certificates in the country – was able to respond fully to a Freedom of Information request asking for numbers of licence holders with convictions.
Staff at the region's largest force, West Yorkshire Police, said they would need about 1,000 hours to retrieve the information, while other constabularies admitted it would take them even longer.
West Mercia Police said the search would take more than 7,800 hours to complete – the equivalent of three years and nine months, if researchers work a typical 40-hour week.
Sixteen police forces revealed that they had stripped gun owners of their licences in the last two years for reasons including criminal convictions, failure to properly store weapons, disputes with neighbours and ex-partners, and mental health concerns.
Select Committee chairman Keith Vaz said: "The terrible murders perpetrated by Derrick Bird in June highlighted gaps in the current licensing regime, notably around the ease with which convicted criminals can gain access to firearms."