In the past few weeks questionnaires have been sent to all 51 chief constables on behalf of the Association of Chief Police Officers, asking whether they would support a nation-wide amnesty. So far almost all of them have given their backing to such a scheme.
Later this week Acpo will decide whether to urge the Attorney General, Sir Nicholas Lyell, to allow an amnesty from prosecution. There are no accurate figures available for the number of illegally held firearms, but estimates have varied from 500,000 to more than 1 million.
An amnesty would have little effect on criminals - many of whom often get their guns on the black market - who would be unlikely to hand in their weapons. However, it would reduce the number of guns in circulation.
A factor against a national scheme is the high cost of organising and running such a high-profile project. In the last national amnesty, held in 1988 after the Hungerford massacre in which 17 people died, 48,000 firearms were surrendered.
The Home Office may feel another amnesty so soon would be a waste of resources. Like then, the one-month scheme would probably involve the anonymous surrender of unlicensed firearms to police stations.
The guns would be handed in under the assurance that no one would face criminal charges. The police would also agree not to carry out any forensic tests to link specific guns with known crimes.
The Firearms Consultative Committee, which has representatives of gun users, the police, the Home Office and Crown Prosecution Service, also recommended an amnesty on electric stun guns and large-magazine smoothbore guns. However, any amnesty would not solve the problem of unmarked guns that that are kept by criminal quartermasters for hire to other villians.
Many weapons are being brought in from Eastern Europe, with wars in places such as the former Yugoslavia providing a ready supply.
Slackening border security in places such as the former Soviet Union has also helped. An ACPO spokesman said: "Any scheme would be incredibly resource-intensive, which will have to be taken into account. However it is important to reduce the number of illegally-held guns in circulation."
A Home Office spokesman added: "Our gun laws are among the toughest in Europe, but we will consider any measures that can help further tackle the problem."