The Prime Minister has instructed Mr Clarke to include a "points system" for new arrivals from outside the EU, according to Labour sources.
Mr Clarke will today announce plans to fingerprint everyone who obtains a British visa as well as introducing measures to limit the number of dependents allowed to follow a relative to Britain.
Mr Blair and Alan Milburn, Labour's general election co-ordinator, are understood to have insisted on the introduction of a points system for migrants, despite early misgivings.
The policy changes are understood to be prompted by Labour's fear they might be trumped on immigration by the Tories. Mr Blair and Mr Milburn are said to have been rattled by the Tories' tough line, which includes quotas for immigrants, and told Mr Clarke that he should match their message.
Yesterday the Home Secretary admitted it was "very difficult" to ascertain the number of people who are currently living in Britain illegally.
He will announce his immigration proposals today in the House of Commons, talking up the Government's intention to favour economically beneficial migrants over those who "are a burden on society" and setting out his plans for tougher controls to track immigrants.
"One of the key issues of our proposals tomorrow is to ensure that we are able properly to identify absolutely everybody who comes into the country," he said.
The planned economic test for migrants is likely to prove controversial among race relations campaigners.
Yesterday Trevor Phillips, the chairman of the Commission for Racial Equality, rejected Government claims that Britain's "hospitality" had been tested by abuses of the immigration and asylum system.
"The whole idea that migrants coming into this country are receiving hospitality - tell that to the 44,000 doctors in the NHS and the 70,000 nurses without whom we would really see what pressure on the health service means," said Mr Phillips, on the BBC's Breakfast with Frost. "Ditto the teachers, from South Africa, Australia, Jamaica, who are reducing the sizes of our classes and schools."
The Home Secretary will also focus on asylum seekers whose claims are rejected but disappear.
"A very much larger number of people claim asylum than are in fact entitled to it," he said.
"As they come and claim asylum, we have to be sure that people can't falsely claim, can't come into the country when they ought not to be able to, and secondly, if they appeal for asylum and that is turned down, that they are then removed from the country."
Mr Clarke has also laughed off suggestions of a rift with Alan Milburn. He dismissed reports that Mr Milburn had told colleagues that Mr Clarke's appointment as David Blunkett's replacement as a "mistake".
"Alan and I are good friends. I saw that piece and I did laugh at it. Alan and I work well, we talk well and we have been a good team," he said. "I'm sure he won't have said that. I know he doesn't believe it. And I'm sure it's the kind of thing that he wouldn't say, even if he did believe it," he said on Breakfast with Frost.
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