David Cameron said he wants an immigration system which "puts Britain first", as he unveiled tough new measures which will halve the time migrants from the European Union without serious job prospects can claim benefits in the UK.

The Prime Minister joined Home Secretary Theresa May to meet immigration enforcement officers after a dawn raid which uncovered four illegal Albanian migrants living with a minor in a single bedroom, as well as two visa overstayers.

Mr Cameron said his changes would address what he claimed was the "magnetic pull" of the UK benefits system and would make clear to migrants that they cannot get "something for nothing".

But Labour said it had made similar proposals 18 months ago, and called for "less talk, more action" from the Prime Minister.

The plans will build on reforms announced in January which mean that European migrants must wait three months after arriving in Britain before claiming out-of-work benefits. From November, once that waiting period is over, benefits will be cut off after three months - rather than the current six - unless the migrants have "very clear job prospects" .

No figures were available for the number of migrants expected to lose welfare payments as a result, but the Department for Work and Pensions said some 121,280 EU nationals were claiming working-age benefits in the UK in February last year - up by 4,760 since 2012 and 56,190 since 2008.

Mr Cameron also announced tougher rules to be imposed on universities and colleges which sponsor international students to study in the UK.

From November, the threshold for stripping educational institutions of their "highly-trusted sponsor" status will be cut, so that they lose it if 10% or more of the individuals they offer places are refused visas, rather than the present 20%.

And he highlighted measures, introduced in the Immigration Act earlier this year and now coming into effect, which restrict the abuse of the European Convention right to a family life to avoid deportation and establish a new "deport now, appeal later" approach to foreign criminals. A new power to revoke driving licences of illegal immigrants has been used 3,150 since its introduction earlier this month, he said.

Speaking at the dawn raid site in Slough, Berkshire, after meeting immigration officers, Mr Cameron said: "Our changes today will save the British taxpayer half a billion pounds over the next five years, so that is a significant saving.

"But let's be clear - some people are coming here to work, some people are coming here to claim, some people are coming here pretending to be students. I have a very clear approach to this, which is, if you don't have a right to be here, you will be sent home, you shouldn't be here.

"People want to know that, yes, we have a fair legal migration system but, in terms of illegal migration, we will find you and we will send you home."

He added: "We want an immigration system that puts Britain first and so what we're doing today is a whole series of changes that says to people if you come here illegally we will make it harder for you to have a home, to get a car, to have a job, to get a bank account, and when we find you - and we will find you - we'll make sure you're sent back to the country that you came from.

"And we're also doing more today to close down bogus student colleges. We've already closed down many of them and we will close down more.

"It's really right that the British people know that we have a fair immigration system that says to people if you're here illegally you should go home."

The Government also launched a consultation on banning overseas-only advertising of jobs, by legally requiring employment agencies to seek applicants for posts in Britain, as well as new plans to restrict the number of JobCentre Plus vacancies automatically advertised on an EU-wide employment portal.

Mrs May said: "We are building an immigration system that is fair to British citizens and legitimate migrants, but tough on those who abuse it or flout the law.

"The Immigration Act is a landmark piece of legislation that will make Britain a less attractive place for those who come here for the wrong reasons, and allow us to remove more people when they have no right to remain. "

Shadow home secretary Yvette Cooper said the Government was failing on immigration despite Mr Cameron's promise to get it down to the tens of thousands.

"We need less talk from the Prime Minister on immigration and more action," she said.

"It's almost a year and a half since Labour called for benefit restrictions on new migrants. In that time we've had reannouncement after reannouncement from the Tories but little in the way of firm action.

"Behind the rhetoric, the true picture of this Government on immigration is one of failure, with net migration going up, despite David Cameron's promise to get it down to the tens of thousands.

"The Government should get a grip and finally implement Labour's proposals to stop the undercutting of wages and jobs for local workers by the exploitation of low-skilled migrant labour, including banning recruitment agencies that only hire foreign workers and pressing for stronger controls in Europe."

During this morning's raid, immigration officers found four Albanian men aged between 27 and 31, along with one minor, who all entered the country illegally.

In the same house, t hey detained a Kenyan woman, aged 35, who had overstayed her visa, while at a separate address was a 35-year-old Indian visa overstayer who was in possession of a false Portuguese passport.

A Home Office spokesman said all of them have been taken to immigration detention pending removal from the country, apart from the minor, who is in the care of social services.

Work and Pensions Secretary Iain Duncan Smith said that it was not possible to predict exactly how many people would be affected by the new benefit restrictions, because the previous Labour administration had failed to break down claimant records by nationality.

"All we have at the moment are the figures I've gleaned from the applications for Ninos (National Insurance numbers) but there will be other people who come in and claim," he told BBC Radio 4's World at One.

"The only numbers we've got at the moment which in any way give you any indication were that in August 2013 the number of people who were applying for Ninos who were also at the same time claiming benefit was about 121,000."

Mr Duncan Smith said that the £500 million estimate for potential savings was produced by the independent Office for Budget Responsibility.

He added: "There's a general consensus in countries like Germany and Holland and Spain and all over that there shouldn't be a right just to enter a country and claim benefits unless you've contributed.

"So the eventual plan - and this is where we want to be, and I think there's a lot of general agreement about this - is that people should have contributed to the system before being able to claim anything. At the moment we can only tighten up the system we've got."

Jonathan Portes, director of the National Institute of Economic and Social Research (Niesr), said that the additional restrictions on migrants' benefits would "affect almost nobody and save very little money".

Mr Portes told World at One: "The IMF yesterday released a report on the British economy, which was generally quite favourable, but one thing they said that immigration restrictions - particularly on skilled workers and students - were likely to reduce productivity. They will make all of us poorer, not just the immigrants."

Ukip MEP and party migration spokesman Steven Woolfe said: "Once again we have David Cameron attempting to sound tough on immigration. It is nothing more than a cynical and vacuous attempt to fool the British public.

"Cameron says nobody can be entitled to something for nothing - yet he still wants migrants to be able to claim benefits for three months having contributed nothing. This is the same Government which currently hands out £1.7 million per month to migrant families for free social housing and cannot stop migration from any country inside or joining in the future.

"This is also the same government and same Prime Minister who pledged to bring net migration down to the tens of thousands - but has instead overseen hundreds of thousands net per year continue to flood into an increasingly crowded Britain."

London Mayor Boris Johnson told BBC Radio 4 World at One: "I'm pro people being able to come and make their lives in London if they've got talent and if they've got energy. That's what the city has depended on for 2,000 years. Forty per cent of Londoners were born abroad. It's an amazing melting pot.

"What nobody could want to see is people coming and simply bludging and sponging and all the rest of it, and I think what David Cameron was talking about this morning was completely right."