Mr Johnson said more people should pay taxes
The UK could be home to almost three-quarters of a million illegal immigrants, a study for London Mayor Boris Johnson suggests.
A Home Office estimate in 2001 put the figure at 430,000.
But the study estimated the number of illegal or "irregular" immigrants and their dependents in 2007 to be 725,000.
Mr Johnson said an amnesty for many would be "morally right", but the government warned it would become a "big pull factor" for more immigration.
The study into the economic impact of an amnesty for illegal immigrants was carried out by the London School of Economics (LSE).
It estimates that, if a minimum of five years' residence in the UK were needed to qualify, 450,000 illegal immigrants could be granted amnesty.
Mr Johnson suggested an amnesty, which would offer some the right to work officially and eventually gain full citizenship, during the 2008 mayoral election.
In an interview for Monday's Panorama on BBC One, he said: "If it does look as though they could make a contribution to society, we should regularise their status or offer them the chance of regularising their status."
He added: "There would be some very tough criteria. Obviously no criminal record would be one, an ability to support yourself and support your family, commitment to society and the most, the most important thing is they should have been here for a considerable period of time."
Mr Johnson said it was a "hard political argument to win" but added: "If people are going to be here and we've chronically failed to kick them out it's morally right that they should contribute in their taxes to the rest of society."
The government is now tightening up border controls, introducing the "e-borders" system which counts people in and out of the country.
But at current rates of deportation, using the LSE figure of 725,000, it would take 34 years and cost almost £9bn to clear the backlog of people who are currently in the UK illegally.
Some claim that an amnesty would lure other illegal immigrants to the UK
The idea of an amnesty is not supported by the Conservatives or the government.
Immigration Minister Phil Woolas said such a scheme would encourage more illegal immigrants.
He said: "What unfortunately would happen is that people traffickers and others would see that as a pull factor to get people to the United Kingdom illegally and we would end up with a bigger problem not just for our society, but for the people themselves involved."
He added: "The proposal for an amnesty starts with a conversation in London with the best of intentions and it ends up with dead bodies in the back of lorries in northern France.".
The UK Border Agency (UKBA) said it did not tolerate anyone who abused the system and that the UK had "one of the toughest borders in the world and we are determined to ensure it stays that way".
A spokesperson added: "There is now triple ring of security that protects Britain: fingerprint visas, ID cards for foreign nationals that lock people to one identity and our hi-tech electronic border controls that check people against police, immigration and customs watch-lists and will cover even more passenger journeys by the end of this year.
"We are also taking tough enforcement action. Since the UK Border Agency was launched in April 2008, UKBA staff have made over 4,900 arrests as a result of people encountered during illegal working operations and our tough new force at the border last year stopped over 28,000 individual attempts to cross the Channel illegally."
Liberal Democrat home affairs spokesman Chris Huhne said: "Labour and the Conservatives cannot continue to stick their heads in the sand and ignore the sheer number of irregular migrants residing here.
"Tougher border controls and an earned route to citizenship, long-championed by the Liberal Democrats, is the only way to bring thousands of people out of the hands of gangmasters and criminals and into the hands of the taxman."
Sir Andrew Green, chairman of the Migrationwatch think-tank, opposed the idea of an amnesty, saying: "We have the biggest recession in memory getting under way, two million unemployed, heading up for three million. Is it really suggested that British jobs should go to illegal workers? It just makes no sense at all."
But Austin Ivereigh of Strangers Into Citizens, which campaigns for long-term migrants to be given citizenship, said: "We have to deal with the fact there is a large, undocumented population in this country who are here because they came through the asylum system or because they came to study.
"They've ended up here. They've put down roots. Their children are in our schools. They're often working.
"And we need to call them out of the shadows so they can play their part in society, they can pay taxes. This is a move that benefits everyone."
Immigration - Time for an Amnesty? Panorama: 9 March 2008 on BBC One at 8.30pm.