"There are no official estimates of the number of illegal immigrants into the United Kingdom," Mr Blair told parliament where the opposition Conservative Party seized on the issue.
"By its very nature illegal immigration is difficult to measure and any estimates would be highly speculative."
Immigration minister Tony McNulty told BBC television later that the best estimate of the number of illegal immigrants, which was "roughly in the ball park," was between 310,000 and 570,000, and it could take ten years to deport them.
Identity cards
Mr Blair sought to use the issue, which dominated the morning newspapers and radio talk shows, to promote his controversial plan to introduce ID cards for everyone in the country.
"We need identity cards both for foreign nationals and for British nationals," he said. "If we want to track people coming in and out of our country and know the identity of people here, that is what we have to do."
But with his popularity among voters at its lowest point since he came to power nine years ago, and his Labour government ensnared in several furores, Mr Blair was left on the defensive.
In a testy exchange across the floor of the lower House of Commons,
Conservative leader David Cameron said the prime minister sounded "rattled" and that the government was in "paralysis".
The immigration flap grew out of an admission on Tuesday by Dave Roberts, the Home Office official in charge of deportations. He told a parliamentary committee that he did not have "the faintest idea" how many illegal immigrants were in the country.
Political analysts were not too surprised, given that visitors to Britain go through immigration controls only when they arrive, and that there has never been a peacetime ID card system as in continental Europe.
Losing authority
Technically speaking, an illegal immigrant could easily be a well-heeled young American student who overstays his or her visa.
But for many native Britons, the phrase brings to mind failed asylum-seekers from the Middle East and Africa who ignore their deportation order, disappear into their ethnic communities and try to earn a living on the black market.
The government’s admissions, concerning an issue that many Britons consider a major concern, only fed the notion that Mr Blair is gradually losing his authority.
"Whether it is deporting dangerous criminals, sorting out the mess of the Human Rights Act or dealing with illegal immigration, this is a government in paralysis," said Mr Cameron, whose Conservatives now lead Labour in opinion polls.
In recent weeks Mr Blair has been facing uproars over the Home Office's failure to consider more than 1,000 convicts of foreign nationality, some of them hardened criminals, for deportation after they served their prison terms.
Police are meanwhile looking into the nomination of wealthy Labour supporters to the House of Lords, the unelected upper chamber of parliament, after they made loans to help the party win the May 2005 general election.