Gun laws will not be reviewed in the wake of a man with a gun licence shooting himself and three female relatives in Peterlee, County Durham, the government has said.

"The firearms laws we have in place are among the toughest in the world. The purpose of that legislation is to protect public safety and at the same time, ensure that controls are practical and proportionate," a Downing Street spokesperson said on Tuesday.

But home affairs select committee chairman Keith Vaz called for gun laws to be "simplified, clarified, and made consistent" so they could be better understood.

Police plan to investigate why Michael Atherton, 42, who killed his partner, her sister and his niece was allowed to hold licences for firearms and shotguns.

Atherton held a licence for three "section one" firearms, which require extra vetting from the police.

The British Association for Shooting and Conservation (BASC) have called for the "facts" in the case to be looked at before drawing any conclusions.

"There has just been a comprehensive parliamentary review of firearms law in the UK and the facts in this incident need to be firmly established."

During prime minister's questions in September 2011, David Cameron said he would happily toughen gun laws if it was needed.

In answer to a question about children holding gun licences, the prime minister said: "I think we should enforce proper rules on gun licences, including shotgun licences. We always keep these rules under review and if they need toughening, I will happily look at that."

The UK's gun licence system requires background checks and reviews at five-yearly intervals.

Responding to Number 10 David Taylor, Shooting Campaign Manager for the Countryside Alliance, said the group were pleased that the government was taking time to consider what had happened in Peterlee.

"The laws that govern shooting have been carefully drawn and added-to over several years so that today they are as rigorous and all-encompassing as possible. There looks to have been a failure at some point in the process in this event, and the most sensible action is to investigate what went wrong and then decide how it might be fixed.”