Interviewed on Newsnight on BBC Two, the Prime Minister said that it was “pointless speculating” about numbers and denied that he had lost control of the country’s borders.

In a 30-minute interview with Jeremy Paxman, Mr Blair maintained several times that just as the previous Government had been unable to give numbers, neither could he.

Paxman asked at least 20 questions aimed at persuading Mr Blair to give an answer but each time he refused and both of them became increasingly exasperated. As the encounter continued Mr Blair declared that he did not make a “working assumption” of the numbers but the system had been hugely tightened up.

“I can’t be sure of the numbers of people who are illegals in this country, for the same reason that the previous Government couldn’t,” he said.

There are no official estimates of the numbers of illegal immigrants in Britain but the Home Office has asked academics to come up with methods of putting a figure on it. An estimated 308,000 asylum-seekers have been refused permission to stay since 1997 but only 72,000 of them are recorded as having left the country.

Mr Blair also denied that taxes would have to rise. “You are going to have to raise taxes after the election, aren’t you?” Paxman asked. Mr Blair replied: “No, you can’t say that on the basis of the spending plans we have. The spending proposals we have are adequately catered for by the tax plans we have got.”

Earlier in the interview, Mr Blair acknowledged trust would be an issue in the election after the Iraq war, but he defended his decision to remove Saddam Hussein.

The grilling came on the day that Mr Blair ran into a difficult confrontation with a disillusioned Labour voter who told him that he had turned a Tory government into a Labour one.

After criticism that he had been kept away from contact with real voters Mr Blair ventured into a Leeds shopping centre — and ran into a volley from the 20-year-old daughter of a former Labour councillor. Jessica Haigh told Mr Blair she would be voting Liberal Democrat because of issues such as the Iraq war.

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