Jeremy Corbyn will face fresh pressure over EU immigration when a challenger to run Britain’s biggest union warns its members will “feel betrayed” unless curbs are introduced.

Gerard Coyne – who is seeking to topple Unite chief Len McCluskey, the Labour leader’s power broker – will vow to make post-Brexit restrictions on free movement a key plank of his manifesto.

In a speech on Monday, the man seen as a centrist candidate will call for “control of our borders” to be a red line in the looming negotiations on EU withdrawal.

With EU leaders insisting members of the EU’s single market must accept free movement of citizens, Theresa May should therefore rule out remaining in the trading arrangements, he will say.

The call will see Mr Coyne echo the stance of Conservative Brexit supporters, who are urging the Prime Minister to stick to her stance of no compromise over the need for immigration restrictions.

And it will put him at odds with Mr Corbyn, who has suggested the free movement of workers across the EU should continue after Britain’s exit.

As The Independent revealed last week, the challenger believes he can defeat Mr McCluskey with a higher turnout of Unite members, a result that could fatally weaken Mr Corbyn’s position.

Speaking in Birmingham, Mr Coyne will argue that lower immigration was – with the much-ridiculed pledge to give an extra £350m a week to the NHS – the key promise made by the Leave campaign.

And he will say: “There is one principle on which the UK Government should not even begin to negotiate. That is over the question of control of our borders.

“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, the union’s regional secretary in the West Midlands, will argue that 2.9 million EU nationals have brought “huge benefits” in public services such as social care, for example.

But he will say: “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.

“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.”

He will call on Ms May to make the issue “non-negotiable”, adding: “There can be no compromise on the principle of taking back control of our borders.”

Mr Coyne’s stance goes much further than Mr McCluskey, who said Unite must listen to the concerns of working people about free movement, but denied he was calling for it to end.

Candidates for general secretary must gather nominations from at least 50 workplaces or branches by 17 February, with the vote to take place between late March and mid-April.

The leadership race was triggered by Mr McCluskey resigning early, in the hope of winning again and staying in charge until 2020 – heading off pressure to retire in 2018, when his term ended.