Top Government ministers have ruled out forcing companies to publish lists of their foreign workers, as a former Tory cabinet member suggested plans to collect the data were "repugnant".
Defence Secretary Sir Michael Fallon and Education Secretary Justine Greening insisted the information was aimed at improving Government investment in skills training, and said it would never be made public or used for "naming and shaming".
The plans were announced at the Tory party conference by Home Secretary Amber Rudd and have been widely condemned, with Labour calling them "xenophobic".
Business groups rounded on the plans, while David Cameron's former senior adviser Steve Hilton branded them "divisive, repugnant, and insanely bureaucratic" - a view shared by former education secretary Nicky Morgan.
Asked on the Murnaghan programme on Sky News if she would endorse Mr Hilton's view of the policy as repugnant, Ms Morgan said: "Yes, I probably would, actually. I think it's a really inadvisable way to proceed.
"I was surprised that Amber had put forward that proposal about the listing of foreign workers, because that's not the Amber Rudd I know and worked alongside in the cabinet.
"The trouble with these sorts of policies is that they send out a message about the party, about the way we want to approach people coming to this country, bringing their talents, their skills here.
"I don't think that's a message we want to send out to the wider world."
However, both Ms Greening and Sir Michael said the policy had been misinterpreted.
Ms Greening told ITV's Peston On Sunday: "This is not data that will be published. There will be absolutely no naming and shaming.
"This is about informing policy, so that we understand particularly which areas and parts of the country there are skills shortages, evidenced by the fact employers are not taking local workers as much as they might do.
"It enables us to tailor policy in those areas so that we can respond to that and make sure that people can take advantage of the opportunities economically in their area.
"We're not going to get smart policy if we don't have the right evidence to be able to drive. That's what this is all about."
Sir Michael added the plans were only a small shift in policy compared to the information companies already gather when employing workers from overseas.
As part of the Resident Labour Market Test, companies have to advertise the position in Britain for 28 days, then they have to demonstrate there was no British applicant who could fill the post.
Sir Michael told Pienaar's Politics on BBC Radio 5 Live: "We're looking to see whether that is just box ticking, or whether we can get a better picture of exactly what the dependence on foreign workers is in each particular sector.
"That would mean, for example, asking companies to simply report their numbers, which we wouldn't publish or identify.
"But it would be interesting to know whether, for example, the fishing industry had a very high dependence on foreign workers, or the agriculture industry, or the banking sector.
"That would enable us to look again at the courses the local colleges were offering and to make sure companies were treated fairly.
"We will not be asking companies to list or name, to publish or identify in any way the number of foreign workers they have. It's been slightly misinterpreted."
Mr Hilton, who broke away from former prime minister Mr Cameron to back Brexit, was scathing about the foreign worker list suggestion in an article for the Sunday Times.
He wrote that ministers might as well announce that "foreign workers will be tattooed with numbers on their forearms".
Ms Rudd told people not to brand her a "racist" after the idea was widely condemned.
The initiative was also attacked by Ukip MEP Roger Helmer, who said: "This idea that companies should provide lists of foreigners - if we had suggested that, if Ukip had suggested that, they would have been shouting 'fascist' up and down the street. I personally think that is a step too far."
A Home Office spokesman previously said: "This is not about listing foreign workers or so-called naming and shaming of companies. The proportion of international workers in a company is one of the pieces of information that companies may be asked to provide to the Government.
"This information will not be published. This already happens in the US and is one of several proposals we will be consulting on as part of our work to ensure that companies take reasonable steps to recruit at home before looking to bring in workers from abroad.
"The purpose of having a consultation is so that we can listen to business and use that feedback to inform our decisions."
A Home Office source said: "This is a wilful misinterpretation of one question in a consultation document - the whole point of which is to seek views on the best approach."
Shadow home secretary Diane Abbott said: "The Tories are in disarray following Amber Rudd's worrying statement last week, contradicting each other as their policy falls apart at the seams.
"The Tories' anti-foreigner agenda is a distraction from their own complete failures of policy, and against the best interests of society.
"Many sectors risk collapse if the Tories press ahead with these plans on overseas workers: the City, farmers, the NHS, construction.
"We need answers from the Tories on how they will protect our economy, but they have no plan other than a risky hard Brexit, which would threaten our prosperity."
A CBI spokesman said: "We welcome the Government's positive announcement that firms will not be required to list their foreign employees.
"Business and the Government need to work together to grow the skills needed for a thriving economy.
"The £45 billion business invests in training each year must complement education and skills development in schools, further education and higher education.
"This will give us the foundation to develop an approach to migration that both supports the economy and deals with public concerns in the long run.
"However, there are skills and labour gaps in the economy right now. If firms do not plug those gaps, they cannot grow, create jobs and spread prosperity - something that must be recognised in the short term."
Liberal Democrat leader Tim Farron said: "The Conservatives are lurching from one damaging announcement to another, making the pound crash and foreign workers feel unwelcome.
"Even Conservatives described the plan as repugnant. It is clear Theresa May is happy to dance to Ukip's tune and only ask the difficult questions later.
"The Conservatives are reckless, divisive and uncaring. With Labour saying they did not object to this disgusting plan in principle, the Liberal Democrats are now the real opposition to the Conservative Brexit government."