People in England and Wales have two weeks to hand in guns, other weapons and ammunition to police stations without being punished for possession.
The National Ballistics Intelligence Service (Nabis), which is co-ordinating the surrender, says many firearms are held in ignorance of their illegality.
Anyone handing in weapons will not automatically be charged, but will be if they are later connected to a crime, according to a BBC report.
Police say the UK-wide surrender campaign is aimed at the "full spectrum" of society.
Helen McMillan, National Police Chiefs' Council firearms lead, said: "You don't have to give your name or address, we just want more guns out of harm's way."
BB-guns, air weapons, rifles, shotguns or pistols are among the weapons police say should be handed in by the 26 November cut-off.
Police think some people come across weapons when clearing the houses of relatives and may not know what to do with them.
'Save a life'
Ms McMillan said: "It could be a trophy of war, it could be a starting pistol - please contact us on 101 and arrange to hand it in to your nearest police station."
She added: "Each firearm we retrieve has the potential to save a life so do the right thing and surrender your weapon."
After the last gun surrender in England and Wales in 2014, more than 6,000 weapons were handed in.
Detective Chief Superintendent Jo Chilton, head of Nabis, said: "Surrendering unwanted or illegal firearms avoids the risk of them becoming involved in crime."
Figures from the Office for National Statistics show that crime involving firearms in England and Wales increased by 27% in the year to June 2017.