Carolyn Fairbairn, head of the Confederation of British Industry (CBI), has described the lack of direction over the future of EU citizens as "intolerable".
The rights of people affected by Brexit, both in the EU and the UK, is top of the agenda in divorce talks, but the negotiating teams have not yet made a breakthrough.
Talking about immigration at a Conservative party conference event this morning, Fairbairn said it was the "number one" issue for businesses.
"If I could pick one word to describe how firms feel about this it is despair, absolute despair," she said.
"The number of firms who put that issue top of the list - forget the other issues about Brexit - it is number one, and we are hearing stories now of firms whose workers are not coming back after summer. They are just not coming back."
She said it was unacceptable that the EU citizens living in the UK still did not know whether they would be given the right to stay.
"It is about our brand image globally, it is about the kind of country we want to be," she said. "And I don’t think there is enough understanding of the urgency of this issue. It is something that is under our control, it is something we can do something about."
The CBI chief said the government must make difficult choices to achieve the best outcome from Brexit, for example, accepting a transitional deal, which would postpone signing trade deals.
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"And I think that if we are going to remain in the customs union as part of the transition proposal to the European Union that is one of those hard choices - we postpone those conversations," she said. "We have those conversations, [but] we are probably not going to be able to sign them and that is a hard choice."
Ultimately, outlining new free trade agreements was a key opportunity for the UK, she said, because the government will be able to get to grips with its own trading relationships once again.
However, she warned that controversies will arise as the UK seeks new partnerships, as vested interests were likely to react to changes in trade policy.