The UK's National Ballistics Intelligence Service (NABIS), which is coordinating the surrender, says many firearms are held by individuals in ignorance of their illegality.
"Surrendering unwanted or illegal firearms avoids the risk of them becoming involved in crime," said Detective Chief Superintendent Jo Chilton, head of NABIS.
Under the new amnesty period, anyone handing in weapons will not automatically be charged but could face action if those weapons are later connected to a crime.
"You don't have to give your name or address, we just want more guns out of harm's way," said Helen McMillan, the firearms lead for the National Police Chiefs' Council.
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Each firearm we retrieve has the potential to save a life so do the right thing and surrender your weapon," she said.
BB or air guns, rifles, shotguns or pistols are among the weapons police in England and Wales say should be handed in by the November 26 cut-off date.
The amnesty is aimed at people who may accidentally come across weapons when clearing the homes of relatives and may not know what to do with them.
Scotland Yard has launched a social media drive to coincide with the gun surrender campaign in partnership with City of London Police.
"Each firearm we retrieve helps to reduce the threat of gun crime in London,"saidCommander Jim Stokley, of the Metropolitan Police's Trident and Area Crime Command.
"Illegal possession of a firearm can mean five years behind bars, and if you are found guilty of possession with intent to supply, that can lead to an even longer prison sentence," he warned.
Figures from the UK's Office for National Statistics (ONS) show that crime involving firearms in England and Wales increased by 27 per cent in the year to June 2017.