“If you want to control immigration you have to control that bit of immigration you are able to control. It’s still possible to control non-EU immigration.”

The report from the Lords Economic Affairs Committee, which includes economists and two former Chancellors, delivered a crushing blow to the Government after concluding that migrants bring no economic benefit.

It systematically dismissed each argument, including claims that migrants are needed to fill jobs and defuse a future “pensions timebomb”.

It said claims from ministers that immigrants added £6billion to gross domestic product were “’irrelevant and misleading”, pointing out that the “biggest winners” were migrants themselves.

The committee called for an “explicit target range for net immigration”, effectively meaning an annual limit. But Mr Brown insisted the new points-based system is the way forward, despite the Lords report questioning its effectiveness.

He said: “Most people who are proposing a cap are proposing a cap of only 20 per cent of possible migrants. Of course, many of these people are the highly skilled workers who are important to the economy.”

He went on: “I believe most businesses that have faced labour shortages, skills shortages – and in the situation we’ve had over the last 10 years there has been a very high level of vacancies, today there are around 675,000 – know the benefits of being able to recruit more widely.

“But what we have done for the last few months is introduce for the first time a new points system, like the Australian system, that will restrict the non-skilled people that come into this country from outside the European Union.

“What that will effectively mean is not just to put a cap on unskilled entrants into the UK, there will be nobody coming who is unskilled from outside the EU.”

His comments were echoed by Immigration Minister Liam Byrne.

The Lords report had already argued that the very fact job vacancies still exist showed that migrant workers are not the answer, as they only expand the economy, creating new gaps.

The claim that a cap will only affect one in five migrants, because most migrants come from within the EU, was also dismissed in February by the independent Statistics Commission.

It backed Migrationwatch’s argument that the real figure for immigration from outside Europe was more than two-thirds of the total because movements by Britons had been wrongly included in Government estimates.

Shadow Home Secretary David Davis said: “The Prime Minister is in denial. His minister’s previous assertions about this have been shown to be bogus. It’s either a sign of desperation or pure lack of grasp that he is repeating them.”

He added: “The points system is half an answer but it will not control the actual numbers. Our policy would ensure that Britain attracted not only the right people but also the right number of people.”

Mr Brown and Mr Byrne remained adamant the £6billion figure was a “substantial” income, despite the Lords dismissing its relevance. The Prime Minister also said gross domestic product per head, largely seen as a better indicator, had risen dramatically since 1997, from £13,900 then to £22,840 in the last year. But figures have already shown that the contribution to that from migrants is less than 60p a week.

Mr Brown said: “We have got to recognise that we’ve got to get the balance right, between the skills that our country gains from people who have these skills coming to our country and being able to offer them to our economy.

“I think most people in the City know we have benefited very substantially, not just from the inward investment that’s coming from international companies, but from key workers who come in. But we want to get the balance right.”