No 10 says UK firearms regulations are arguably the world's toughest but Home Office is accused of codification delays
The government says it has no plans to tighten or review gun laws following the shootings in County Durham in which four people died, saying the UK's current legislation on firearms is arguably the toughest in the world.
Police are investigating the deaths of three women and the man thought to have shot them in the village of Horden on New Year's Day.
They are expected to focus on why the man, Michael Atherton, had been allowed to hold six gun licences.
Downing Street said it needed to protect public safety and ensure controls are practical, but questions remain over why the owner of six guns was not checked after he admitted he had self-harmed.
Keith Vaz, the chairman of the home affairs select committee, said he was writing to Theresa May, the home secretary, to ask what progress she had made in responding to his committee's call a year ago for codification of the 34 separate pieces of legislation covering UK gun law.
He said he was not seeking tougher gun laws but his committee had called for the government to follow a Canadian example whereby the partners of gun applicants are consulted before a licence is provided or renewed.
He also criticised the fact the Home Office had taken nine months to respond to this original report, and still said it was consulting on some of its proposals.
Vaz said: "I am not calling for tougher legislation, I am calling for the existing laws to be codified and clarified so they are understood."
Grahame Morris, the Labour MP for Easington, the constituency in which the incident occurred, said the police had been in an invidious position.
He called for people to have patience and await the report of the Independent Police Complaints Commission.
He praised the police for referring their decision to renew 42-year-old Atherton's gun licence three years ago, even though they were aware he had said he had suicidal tendencies.
Morris said: "I am sure that will be one of the main focuses of the inquiry as to whether more could have been done to identify whether Mr Atherton was right to hold a licence."
He added: "There are bigger issues raised by this awful tragedy ? whether it is appropriate to have firearms stored in a house and whether there should be some professional input into whether someone is in a mental state to be issued with a firearm licence."
Morris called for a sense of proportion but added "public safety must be paramount".
He also said he did not think professional help should be sought by the police on a routine basis.