THERESA May’s government has been accused by Labour of being “in disarray” after it dramatically dropped a controversial plan to force British businesses to publish lists of their foreign workers.

Last week at the Conservative Party conference, Amber Rudd, the home secretary, warned that foreign workers should not be able to “take the jobs that British people should do” and unveiled a plan to make firms publish the proportion of “international staff on their books”.

The proposal caused outrage and was condemned from within and outwith the Tory party as a bid to “name and shame” businesses, which took on large numbers of migrant workers.

Read more: Theresa May under pressure to end 'alarm and uncertainty' over Britain's move to full Brexit

Critics, including Nicola Sturgeon and Kezia Dugdale, branded the plan “disgusting” and “xenophobic”. SNP MP Mhairi Black even suggested Conservatives were now coming up with immigration policies "reminiscent of early 1930s Nazi Germany".

Over the weekend, Steve Hilton, David Cameron’s former policy chief, denounced the foreign workers’ list idea as “repugnant,” a sentiment shared by Nicky Morgan, the former education secretary, who stressed that it would be “inadvisable” to proceed with it.

After five days of ferocious onslaught against the policy, Justine Greening, the education secretary, took to the airwaves on Sunday to announce that the migrant workers’ lists would not be made public but would remain confidential and simply used as an aid to help ministers identify skills shortages.

She told ITV’s Peston on Sunday: "That is really about collecting the right evidence we will need if we're going to be able to respond to skills shortages of employers...This is not data that will be published; there will be absolutely no naming and shaming,"

Read more: Theresa May under pressure to end 'alarm and uncertainty' over Britain's move to full Brexit

Asked if this meant none of the information compiled would be publicly available, Ms Greening replied: "Correct. This is about informing policy so 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 and it then enables us really to tailor policy in those areas so we can respond to that and make sure people can take advantage of the opportunities economically in their areas.”

Her remarks were later echoed by Sir Michael Fallon, the defence secretary, who told BBC Radio 5Live: "What I can absolutely rule out is that we will not be asking companies to list or name or publish or identify in anyway the number of foreign workers they have."

But the announcement did not end the criticism.

The First Minister tweeted: “The fact that the lists would be secret rather than public doesn't make it acceptable. It really doesn't.”

Read more: Theresa May under pressure to end 'alarm and uncertainty' over Britain's move to full Brexit

Diane Abbott for Labour denounced the UK Government's “anti-foreigner agenda,” saying: "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 shadow home secretary added: “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.”

Tim Farron, the Liberal Democrat leader, accused the Conservatives of being “reckless, divisive and uncaring,” and of “lurching from one damaging announcement to another, making the pound crash and foreign workers feel unwelcome”.

Meantime, the education secretary also appeared to retreat on another controversial proposal as she played down reports that foreign academics had been banned from helping give advice to Whitehall on the Brexit negotiations.

However, Ms Greening made clear overseas advisers were “absolutely” welcome to advise the UK Government as long as they had the necessary security checks.

Earlier, it emerged the Scottish Labour leader had written to Boris Johnson, the foreign secretary, seeking clarification on the subject, noting how there was “widespread revulsion at the insular and intolerant direction the UK government appears set on taking”.