Sadiq Khan, the mayor of London, said the proposal sends a “deeply worrying message.”
Nicola Sturgeon, the first minister of Scotland, tweeted a picture of Wednesday’s newspapers and said, “Depressing doesn't even begin to cover it.”
Adam Marshall, acting director general of the British Chambers of Commerce, told the BBC that it would be disappointing for businesses if having a global workforce was seen as "a badge of shame."
The concerted pushback follows a speech by Rudd at the annual Conservative Party conference, where she told the party faithful that Britain’s June 23 vote to leave the European Union was driven “in large part” by high levels of immigration.
The government wants net migration — the number of people arriving minus the number of people leaving — reduced to the “tens of thousands.” Last year, it was nearly 330,000, with about half coming from the E.U.
Prime Minister Theresa May recently said that Britain will start the process of leaving the E.U. no later than the end of March. But the process could take up to two years or more, and while Britain is still a member of the bloc, there is little it can do about controlling immigration from the E.U.
Rudd said that Britain still wants to “attract the brightest and the best” but that it also wants to curb net migration “in the long term, by reducing the numbers that come from Europe” and “in the mid-term, by reforming the student and work route of entry.”
The other proposals she outlined Tuesday include immigration checks for taxi drivers and tightening restrictions for international students. She also said that landlords who knowingly rent out property to illegal immigrants could go to prison.
One of Britain’s top scientists said the proposals were “deplorable.”
Astronomer Martin Rees told the BBC’s "Newsnight" program: “I thought Amber Rudd’s speech was deplorable, and it will lead to difficulties. People won’t feel welcome and won’t want to take jobs here.” He added, “U.K. science has greatly strengthened in the past 20 years. It will be very sad if this is jeopardized by limiting immigration.”
Rudd seemed to soften her position on Wednesday. When asked whether her proposals to force companies to publish the number of foreign workers they employ amounted to “naming and shaming,” she told the BBC that it was just an idea under consideration.
“It’s not something we are definitely going to do. It’s one of the tools we are going to use as a review to see if we can use it as a way of nudging people to do better behavior,” she said.
But Rudd said the government wanted to encourage businesses to hire more local staff and insisted that people need to be able to talk about immigration without being labeled a racist or xenophobe.
"We mustn’t ignore the fact that people want to talk about immigration,” she said. “And if we do talk about immigration, don't call me a racist."