Laws which came into force on 14 July have tightened ownership rules for antique firearms and anyone storing weapons for someone else.
Sussex and Surrey Police forces said guns or ammunition could be handed in under an 11-day amnesty.
It lasts until 21 November and owners would not be prosecuted.
But police said weapons could be analysed to determine if they had been used in a crime.
Chief Supt Paul Morrison said: "We would encourage people to check their attics, sheds and cupboards and hand weapons in.
"A firearm might not be a danger in your hands but if it was stolen by a burglar and passed to other criminals it could put people's lives in danger."
Police launching a gun amnesty in Surrey and Sussex say a law change may mean many people are now holding illegal firearms.