Workers will feel "betrayed" if Britain does not take control of its borders after it quits the European Union, the challenger vying to take over the country's biggest trade union will warn.
Gerard Coyne said the Government should "not even begin to negotiate" over immigration as it attempts to thrash out a Brexit settlement.
The warning from the leadership candidate, who is vying to oust Len McCluskey, one of Jeremy Corbyn's closest allies, as general secretary of Unite, comes as Labour divisions continue to rage over freedom of movement.
Mr Coyne, Unite's West Midlands regional secretary, will say migration within the EU has benefited those who are better off by allowing them to hire low cost cleaners and nannies but has put pressure on services and housing for many others.
Prime Minister Theresa May must say now that curbing freedom of movement is non-negotiable and that will inevitably lead to the UK's exit from the single market, he will tell Unite members at a speech in Birmingham.
"The better off have been able to hire Europeans as their cleaners, or nannies, and have their cars washed at little cost, by people eager to work and prepared to accept what are, by UK standards, low wages," he will say.
"But for the many Britons facing insecurity in the job market, who rely on public services such as the NHS and state schools, and who need affordable homes, the presence of a very large number of foreign nationals has added to the pressures they already face at a time of austerity.
"Theresa May and other ministers should not wait until Article 50 has been triggered to set out a negotiating position on free movement of labour. They should be saying now, without equivocation, that the issue is non-negotiable. There can be no compromise on the principle of taking back control of our borders."
Labour's immigration policy has been in disarray for months as senior figures have repeatedly appeared at odds over the party's approach to the issue.
Shadow Brexit secretary Sir Keir Starmer reiterated his calls for curbs on freedom of movement, insisting it was time for a "fundamental rethink of immigration rules", in an interview with the Sunday Times just a week after the Labour leader indicated he wanted the policy to continue after Brexit.
"My many conversations with Unite members leave me in no doubt that those who voted for Brexit expect that promise of an end to uncontrolled immigration from the EU to be kept, and will feel betrayed if it is not," Mr Coyne will say.
"Let us not fool ourselves. Brexit means exit. It means a world in which we have to be competitive enough to thrive outside the single European market."
Mr McCluskey's five-year term was due to end in 2018 but he opted to bring the election forward by a year to spring.