A large majority of British residents are against offering an amnesty to illegal immigrants
The YouGov survey for the think-tank MigrationWatch, which campaigns against mass migration, suggested 72% opposed the move, with 11% in favour.
Three-quarters of the 2,400 people surveyed felt too many immigrants were coming to the UK.
Immigration Minister Liam Byrne last month refused to rule out an amnesty but says there are no plans for one.
Responding to the new poll, Mr Byrne said the government remained committed to removing people who were in the UK illegally but it welcomed legal migrants.
"The intention of the government's policies is not to increase or reduce the number of people coming to the UK," he said.
"Rather, its aim is to ensure that those who can contribute most to the UK are selected for entry and that the country takes in only as many people as our economy needs at any one time."
But Tony Blair this week said that allowing illegal immigrants to stay in the UK would mean "a lot more" would come.
Sir Andrew Green, chairman of MigrationWatch, told BBC Radio 4's Today amnesties simply did not work.
"There have been five amnesties in Italy in the last 20 years and six in Spain and each time there have been more applicants so that's practical proof that amnesties encourage more illegal immigration," he said.
Amnesties were also expensive, he said. While £500m might be gained from people beginning to pay taxes, the net cost was between £500m and £1bn a year because people began claiming benefits.
Sir Andrew said there should be tougher penalties for employers hiring illegal workers.
That would make work for illegal immigrants dry up and they would then "drift" away.
If they did not, then the situation would remain the same but not get worse.
There could be a three-month period where anybody would be allowed to leave Britain without being arrested for immigration offences.
Seven out of 10 against amnesty for illegals
'Britons against immigrant amnesty'