The thought of having to pay £1000 a year for every EU national they recruit has not gone down well with UK businesses, with the British Chambers of Commerce (BCC) describing the proposal as harmful.
The idea of an immigration skills levy on EU workers has been put forward by Home Office Minister Robert Goodwill, who told the House of Lords' Brexit sub-committee that such a levy would be "helpful to British workers who feel they are overlooked" in favour of migrants.
BCC Director General Adam Marshall responded to the announcement by pointing out that employers are already struggling to find all the skills they need and the minister's idea would simply add unnecessary expense and bureaucratic obstacles to hiring the people that companies require to fill these gaps.
Especially, he went on, as the unwelcome Immigration Skills Charge (of £1000 a year) is already due to come into effect later this year for non-EU workers.
The proposal also drew criticism from the Institute of Directors (IoD) with Head of Employment and Skills Policy, Seamus Nevin, urging the Government to reconsider.
"Businesses are already working with ministers to improve the home-grown skills supply," he said, "but this tax will only damage jobs growth at a time when many businesses are living with uncertainty."
Faced with this level of business opposition, the Prime Minister's office said that Mr Goodwill's idea had been misinterpreted and that the Government is looking at a whole range of options to control immigration once the UK leaves the EU.