One former Conservative Cabinet minister said the move sent out the “wrong message” after ministers had raised the prospect of “naming and shaming” firms that employed too many foreign staff.
And a group of leading Scottish artists and academics have today published an open letter condemning the approach taken by the Tories at their party conference last week where the plans first emerged.
Senior government figures yesterday moved to rule out the prospect of foreign worker lists being made public. The information will still have to be provided to the government, but it will remain confidential.
The climbdown comes as Prime Minister Theresa May faces growing pressure to set out her plans for Brexit with demands in the House of Commons from a cross-party alliance of MPs, including Tory backbenchers, for a vote on the issue.
Former Labour leader Ed Miliband is understood to have gathered support from the SNP and Liberal Democrats for such a move, which would call on Mrs May to set out her “opening terms” for negotiation on leaving the EU.
The foreign workers lists have prompted a furious response since they were raised last Wednesday, with First Minister Nicola Sturgeon even announcing she would back Scottish firms who defied the rules.
Defence Secretary Sir Michael Fallon and Education Secretary Justine Greening said yesterday the information was aimed at improving government investment in skills training - but insisted it would never be made public or used for “naming and shaming”.
Former education secretary Nicky Morgan was among the critics of the proposed lists.
“I think it’s a really inadvisable way to proceed,” she said. “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 said: “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 which parts of the country there are skills shortages, evidenced by the fact employers are not taking local workers as much as they might do.
“We’re not going to get smart policy if we don’t have the right evidence. 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 went on: “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.
“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.
“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.”
Ms Rudd told people not to brand her a “racist” after the idea was widely condemned.
SNP MP Stephen Gethins has today tabled an Urgent Question in the House of Commons seeking an update on Brexit negotiations.
“Mrs May says she will not give a running commentary – but it is starting to look like she has lost grip of all her warring ministers who are fighting like cats in a sack,” he said.
Mr Miliband has held talks with pro-EU Tory MPs on trying to force Mrs May to allow a vote by MPs on any moves to exit the single market. A loose cross-party alliance of pro-Europe MPs from all sides of the Commons has expressed concern at the sudden pace towards a “hard Brexit” stance by the government.
Mr Miliband is considering tabling an urgent Commons question demanding the Prime Minister sets out to parliament exactly what its role will be in the major decisions surrounding Brexit.
The former Labour leader, and ex-Lib Dem head Nick Clegg, are understood to have formed common ground with the SNP, the Greens, and some Tories to seek a strong voice for the Commons in the Brexit process.