Employers will have a transition period before being forced to make immigration checks on EU citizens in the event of a no-deal Brexit, the government has said, contradicting comments from the immigration minister, Caroline Nokes.

The home secretary, Sajid Javid, told ITV’s Peston there would be a “sensible transition period” for EU citizens should an agreement not be reached. “We’ve just got to be practical,” he said.

Downing Street confirmed Javid was right to say a transition period would be a likely solution to help employers adapt to new immigration enforcement, contradicting Nokes’s remarks.

In a statement sent to campaign groups, the Home Office confirmed employers would still have to carry out the normal checks – requiring EU citizens to present a passport or ID card when they seek work – but they would not have to work out whether an EU citizen had just arrived in the country or been living in the UK for a number of years.

“Employers will not be expected to differentiate between resident EU citizens and those arriving after exit,” the Home Office said.

The statement put further pressure on Nokes, who made the error when questioned by the Labour MP Yvette Cooper at a select committee meeting on Tuesday.

“If somebody hasn’t been here prior to the end of March next year, employers will have to make sure they go through adequately rigorous checks to evidence somebody’s right to work,” Nokes said on Wednesday, in what then appeared to be a new policy disclosure.

Her remarks dismayed organisations including the Confederation of British Industry, the British Chambers of Commerce and trade unions, which said they had received no guidance on what to to do in the absence of a Brexit deal.

The London hospitality sector, for instance, draws 40% of its staff from elsewhere in the EU. The NHS, banking and agriculture would suddenly be burdened with extra requirements, business leaders said.

There was also concern that landlords would be required to conduct checks, leading to the prospect of widespread discrimination against EU citizens who have made the UK their home.

The shadow immigration minister, Afzal Khan, wrote to Nokes demanding she return to parliament to set the record straight. He said in his letter that it was “clear that you provided misleading evidence” and accused the minister of “lacking most basic level of understanding and knowledge of your own immigration policy”.

Nicolas Hatton, the co-founder of the3million, a grassroots organisation of EU citizens living in the UK, said Nokes’s comments had “raised the prospect of widespread discrimination against 3 million EU citizens”. The3million wants the rights of EU citizens to be ringfenced and will take part in a protest in Westminster on Monday.

One of the biggest issues with Nokes’s statement was that EU citizens in the UK do not have any means of proving they have the right to work in the country, as Britain does not require any registration on arrival.

The Home Office is testing a new registration system, but only 924 people secured “settled status” ID numbers in a trial that recently finished in Liverpool.

The Home Office statement issued on Wednesday night said: “We will protect EU citizens’ rights when we leave the EU, in either a deal or no-deal scenario, as the prime minister has made clear. We are considering a number of options for the unlikely event that we reach March 2019 without a deal, and will set out more information shortly.

“Employers already need to carry out right to work checks on EU citizens, as they do with all prospective employees. That will not change next March in the event we leave the EU without a deal. EU citizens will continue to be able to evidence their right to work by showing a passport or national identity card. Employers will not be expected to differentiate between resident EU citizens and those arriving after exit.”

The Institute of Directors wrote to Javid on Thursday, demanding he clarify as a matter of urgency what will be expected from businesses if the UK leaves the EU without a deal.

In a letter seen by the Guardian, Stephen Martin, the IoD’s director general, demanded “comprehensive clarity on the procedure employers would have to follow in this scenario, in the form of public written guidance”.

The absence of a plan “threatens to undermine the trust of EU citizens” as well as limiting businesses’ access to workers, he wrote.