Theresa May’s Conservatives have been accused of peddling myths about foreigners taking British people’s jobs after the party unveiled a severe new immigration crackdown.

Under the plans, firms employing from abroad could have to use tests to ensure foreign workers do not take jobs “British people could do”.

Businesses may even be “named and shamed” by being forced to publish what proportion of their workforce comes from overseas. Foreigners looking for work driving taxis could be faced with mandatory immigration checks and overseas students will also be hit by much tougher rules.

The proposals were met with outrage from business groups and MPs alike, with one politician saying they heralded the return of “the nasty party”.

To applause at Conservative conference, Home Secretary Amber Rudd set out a wide-ranging tightening of immigration rules to drive down the number of new people coming into the country. But the harsh rhetoric provoked an equally strong backlash within moments of Ms Rudd leaving the stage in Birmingham.

Seamus Nevin, head of employment and skills policy at the Institute of Directors, said: “It is clear that immigration will continue to be a major bone of contention between companies and this Government. Businesses know that the EU referendum result means change to free movement of workers from the EU, but people were not voting to make the economy weaker. The evidence is clear that migrants are a benefit to the economy.”

Calling Ms Rudd out on her claim that foreigners could be taking jobs British people might otherwise have, he said: “The UK has a record level of employment, so immigration is not hurting jobs.”

CBI Deputy Director-General Josh Hardie said it was time to be clear about the value of migration to the UK, as well as its challenges.

He said: “Businesses will not welcome further restrictions on high skilled migration from key trading partners around the world, especially as a series of changes were only announced earlier this year.

“At a time when we need strong links globally to seize new opportunities after the referendum, being seen as open to the best and brightest is vital.”

James Pitman, managing director of Study Group, demanded Ms Rudd “be honest” that her drive to tighten rules on foreign students will mean more expensive fees for British students.

He said: “The Home Secretary said today that she will ‘level’ with the British people. Then she needs to be honest that a significant reduction in the number of international students will lead to upward pressure on the fees paid by British students, reduced investment in facilities and cause damage to local economies.”

Liberal Democrat home affairs spokesman Alistair Carmichael condemned Ms Rudd’s speech, claiming that it could have been written by Tory right-winger John Redwood.

He said: “The ‘nasty party’ hasn’t come back, rather it seems it never went away. This speech is exhibit A on how the Liberal Democrats restrained the Tories. Without us they are showing their true colours - reckless, divisive and uncaring.”

Labour’s Andy Burnham said Ms Rudd had “depressingly little to say” about what he called the largest humanitarian crisis since the Second World War and noted that she failed to repeat the commitment to taking a share of adult refugees.

Mr Burnham welcomed a £140m fund announced by Ms Rudd to ease the impact of migration on particular areas, similar to an idea his leader Jeremy Corbyn suggested last week.

But Jonathan Bartley, co-leader of the Green Party, said: “The underlying message of Amber Rudd’s ‘controlling migration fund’ is that migrants are to blame for the problems our country faces. This falsehood must be challenged head on.

“The truth is that the ‘pressures’ she spoke of are not caused by migration, but by the Government’s cuts and failure to invest in vital public services such as the NHS.”

The row was exacerbated on a day when another Cabinet minister, Liam Fox, provoked anger after describing EU citizens living in the UK as a “main card” in Brexit negotiations.

Theresa May in quotes Show all 10 1 /10 Theresa May in quotes Theresa May in quotes On being described by the former chancellor Ken Clarke as “a bloody difficult woman”: “Politics could do with some Bloody Difficult Women actually” Rex Features Theresa May in quotes On keeping secrets even from her husband: “There are some things I am told that I am not able to confide in anybody” Rex Features Theresa May in quotes On the relentless focus on her appearance during a speech at the Women in the World summit: "I like clothes and I like shoes. One of the challenges for women in the workplace is to be ourselves and I say you can be clever and like clothes. You can have a career and like clothes” Getty Images Theresa May in quotes On comparisons to Margaret Thatcher: “I think there can only ever be one Margaret Thatcher. I’m not someone who naturally looks to role models. I’ve always, whatever job it is I’m doing at the time, given it my best shot. I put my all into it, and try to do the best job I can” AFP/Getty Images Theresa May in quotes On her rebelliousness, or lack of, as a teenager: “I probably was Goody Two Shoes at school” Getty Images Theresa May in quotes On being replaced as chairman by Lord Saatchi and Liam Fox in 2003: “Yes, it takes two men to step into the shoes of one woman” AFP/Getty Images Theresa May in quotes What Theresa May said when she was asked about her political ambitions during an interview with Miriam González Durántez, a lawyer married to Nick Clegg, in December: MD: "My very last question is: that little girl who is somewhere there, is she dreaming of becoming the next British Prime Minister?" TM: "She’s dreaming of carrying on doing a good job in the Home Office" Getty Images Theresa May in quotes On not being able to have children: “I like to keep my personal life personal. We couldn’t have children, we dealt with it and moved on. I hope nobody would think that mattered; I can still empathise, understand people and care about fairness and opportunity” Getty Images Theresa May in quotes On whether she can deliver the mandate of the EU referendum: “I think for party members and indeed for others, I would say look at my record. I think they can see that I’m somebody who gets on with the job, but I’m also somebody who says it as I see it and actually delivers on what I say” Getty Images Theresa May in quotes On the equally relentless obsession with her shoes: “As a woman I know you can be very serious about something and very soberly dressed add a little bit of interest with footwear. I always tell women ‘you have to be yourself, don’t assume you have to fit into a stereotype’ and if your personality is shown through your clothes or shoes, so be it” Getty Images

Meanwhile, the Prime Minister herself was accused of “insulting” foreign NHS doctors, after saying they would be in the UK “until” enough British doctors are trained to take positions.

In her speech, Ms Rudd said: “I come here today with a warning to those that simply oppose any steps to reduce net migration. This Government will not waver in its commitment to put the interests of the British people first. Reducing net migration back down to sustainable levels will not be easy. But I am committed to delivering it on behalf of the British people.“

Launching a consultation on entry rules for foreign workers and students, she said tests employers undergo before recruiting from abroad had become ”tick-boxing exercises“ which needed to be tightened and that new tests would seek to ”ensure people coming here are filling gaps in the labour market, not taking jobs British people could do”.

The underlying message of Amber Rudd’s ‘controlling migration fund’ is that migrants are to blame for the problems our country faces. This falsehood must be challenged head on <p>Green Part co-leader, Jonathan Bartley</p>

In a briefing sent afterwards, it was made clear that other measures to be considered would be, “whether employers should have to set out the steps they have taken to foster a pool of local candidates, set out the impact on the local labour force of their foreign recruitment and be clear about the proportion of their workforce which is international, as is the case in the US.”

It came as a report from the LSE’s Centre for Economic Performance found new immigration restrictions on EU workers will damage business and not lead to greater job opportunities for British people.

Ms Rudd assured universities she was committed to helping them attract the best students, but said the current system too often “treated every student and university as equal” and that the Government would look at “tougher rules for students on low quality courses”.

Ms Rudd said: “Foreign students, even those studying English Language degrees, don't even have to be proficient in speaking English. We need to look at whether this one-size-fits-all approach really is right for the hundreds of different universities, providing thousands of different courses across the country.

”And we need to look at whether this generous offer for all universities is really adding value to our economy. This isn't about pulling up the drawbridge. It's about making sure students that come here, come to study.“

She said that from December landlords knowingly renting to illegal immigrants could go to prison, people wanting to get a licence to drive a taxi will have a mandatory immigration check and banks will have to make regular checks to ensure customers are here legally.