Changes to national firearms licensing have been recommended after a review into the Derrick Bird killings.
A report has said the murders could not have been prevented under the current system in England, Wales and Scotland.
One proposal is that GPs be told if a licence is granted so they can inform police of any mental health issues.
Bird killed 12 people, including his twin brother David, in a shooting rampage across West Cumbria on 2 June, before turning his gun on himself.
The independent review was conducted by Assistant Chief Constable Adrian Whiting, of Dorset Police, the Association of Chief Police Officer's (Acpo) lead on firearms licensing.
The government said the UK's "tough" firearms laws were always under review and would be tightened further if necessary.
Giving her reaction, the daughter of one of Bird's victims has said guns should not be kept in homes.
The Acpo review concluded that Cumbria Police acted correctly in granting and renewing firearms certificates to Derrick Bird.
He was first granted a shotgun certificate in 1974, aged 16. His most recent certificate renewal was in 2005 and it was due for renewal on 18 November this year.
ACC Whiting's report said the force and other relevant agencies had no information prior to the shooting rampage which showed the gunman should reasonably have had his certificates revoked and guns seized.
He said: "The arrangements for firearm, shotgun and explosive certification in Cumbria are robust and the people involved have the appropriate knowledge, skills and experience.
"There were no reasonable opportunities for the licensing system to have been the instrument of intervention to prevent the appalling offences subsequently committed."
He said the circumstances of the case did not give rise to any immediately obvious changes to Cumbria police or the law that could have prevented the shootings.
But in the second part of his report, ACC Whiting did go on to make a series of recommendations.
Under the Whiting proposals, family members would be formally asked if an applicant was suitable to own a gun.
Other recommendations included banning people from owning guns if they had received a suspended prison term, which is currently not the case.
In 1990, Bird was convicted of two counts of theft and one of handling stolen goods and sentenced to six months' imprisonment, suspended for 12 months.
Had the sentence not been suspended he would have become a "prohibited person" for five years under the Firearms Act 1968 and would have had to reapply for his shotgun certificate.
ACC Whiting also said the law needed to be clarified around the use of firearms for the humane despatch of animals and pest control after what he described as a "significant" increase in handguns held for such purposes.
The Chief Constable of Cumbria Constabulary Craig Mackey - who ordered the inquiry in the wake of the shootings - supported ACC Whiting's proposals, saying they were "trying to close and limit the opportunities for individuals who are unsuitable to get access to lawfully held firearms".
Crime Prevention Minister James Brokenshire said the government would consider the recommendations carefully.
"We have some of the toughest firearms laws in the world. We keep them under review and we are prepared to tighten them further, if necessary. All options are open for discussion," he said.
But Jude Talbot, the daughter of Michael Pike, shot dead by Bird as he took his morning cycle in Seascale, said while she grew up around shotguns in rural Cumbria, there was no place for them in homes.
She told MPs on the Commons Home Affairs Select Committee, which is reviewing firearm controls: "We should not have guns kept in a dwelling. I see no reason why they can't be kept in a gun club.
"I don't think we should be keeping things that kill and maim in a residential area."
Exceptions could be made for farmers to lock their guns away in an outhouse, she suggested.
The British Association for Shooting and Conservation (Basc) welcomed the report.
Director of firearms Bill Harriman said: "UK gun owners go through an extremely rigorous licensing process to ensure as far as possible that they pose no risk to public safety and keep their firearms secure.
"Sadly, you cannot legislate for the moment when a switch flicks in someone's head."
Another review, of how Cumbria dealt with the shootings from an operational perspective, is currently being undertaken by Assistant Chief Constable Simon Chesterman, of West Mercia Police.
An inquest into the deaths of Bird and his 12 victims is then due to be held.