Up to 570,000 illegal immigrants are living in the UK, according to a new Home Office estimate.
No past estimates of illegal immigrants have been published
It is the first time the government has put a figure on the number of illegal immigrants, something Tony Blair in the past said was impossible.
The Home Office says its best estimate is 430,000 but the number could be between 310,000 and 570,000.
The Tories claim the estimate shows an immigration shambles and say it should have been released during the election.
The Home Office estimate does not include asylum seekers whose claims are being processed, or who are appealing against a refusal.
It was produced by taking the numbers of foreign-born people living in the UK recorded in the 2001 Census and subtracting the estimated number of legal immigrants.
Home Office officials say they have sought to take into account the fact that some illegal immigrants may not have filled in their census forms.
Immigration Minister Tony McNulty said the figures were a "best guess".
"By its very nature, it is impossible to quantify accurately, and that remains the case," he said.
Mr McNulty said the estimate underlined the need for identity cards.
When it was put to him that Spain, which has ID cards, has a higher number of illegal immigrants, Mr McNulty said the UK identity card scheme would involve a more sophisticated national database.
Delayed for election?
He denied the release of the estimate was timed to help push ID cards through Parliament or that they had been held back until after the general election.
During the election campaign, the prime minister refused to estimate the number of illegal immigrants.
"You cannot determine specifically how many people are here illegally," said Mr Blair as he was asked 20 times for a figure in an interview with the BBC's Jeremy Paxman.
Conservative shadow home secretary David Davis said: "This report shows unequivocally that the prime minister was wrong when he claimed it was impossible to know how many failed illegal immigrants there are in Britain.
"The fact that there are over 500,000 illegal immigrants living in this country is a shocking indictment of the total shambles that is Labour's immigration and asylum policy."
Liberal Democrat spokesman Mark Oaten said ministers must seriously consider an amnesty for long-term illegal immigrants, coupled with stronger border controls in future.
He said: "The government has got to face facts.
"The resources don't exist to deport half a million people, and many of these individuals will have been here for years and have children."
During the election campaign, ministers branded "grossly inaccurate" a figure of 500,000 produced for the government by immigration expert John Salt.
Professor Salt himself said it was the result of a hypothetical exercise but he is credited with helping on the estimate published on Thursday.
The chairman of immigration pressure group Migrationwatch, Sir Andrew Green, said: "Having denied it vigorously before the election, the government now admit that the number of illegal immigrants is approaching half a million, or half the population of Birmingham.
"Even this looks like a considerable underestimate with little allowance made for illegal entrants and those who overstay their visas."
But Danny Sriskandarajah, from the Institute for Public Policy Research, said: "Many of these people have probably entered the UK legally but have stayed on, often making important contributions to our economy."