The UK’s willingness to compromise is “not without limits”, Brexit Secretary Dominic Raab will warn the EU in a speech to the Conservative conference.
Mr Raab will vow to take a “pragmatic, not dogmatic” approach to the final phase of talks with Brussels.
But if the EU tries to force the UK into accepting a customs union then it will leave without a deal, he will say.
Later, Chancellor Philip Hammond will use his speech to try to outline plans for raising salaries.
These include a £125m package allowing large employers to transfer up to 25% of their apprenticeship levy funds to businesses in their supply chain from April next year.
The apprenticeship levy is a tax on large companies intended to pay for training at smaller companies, but uptake of the new policy has been slow.
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EU leaders have rejected the Prime Minister’s Chequers plan because they believe it would undermine the single market by allowing the UK to “cherry pick” EU law.
Labour leader Jeremy Corbyn said last week his party would back Mrs May in Parliament – if she agrees to their plan for a customs union with the EU and a Brexit deal that guarantees workers’ rights and protects jobs.
But Mr Raab will use his conference speech to warn there are limits to the UK’s readiness to compromise – and they will not accept a customs union.
Neither will the government agree to anything that divides Northern Ireland from the rest of the UK or makes the country a member of the European Economic Area (EEA) like Norway.
He will say: “We are leaving the European Union in fact, not just in name.
“If an attempt is made to lock us in via the back door of the EEA and customs union… or if the only offer from the EU threatens the integrity of our union, then we will be left with no choice but to leave without a deal.”
Restating his backing for Mrs May’s Chequers plan, Mr Raab will say: “Our proposals would deliver a historic agreement that provides a roadmap out of the EU and a final deal that will be good for the whole country.”
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In his speech, Philip Hammond will attempt to look beyond Brexit, calling on Conservatives to convince voters that their policies will “deliver a better tomorrow for them and their families”.
He will warn that slow wage growth and job insecurity mean too many people fear they are being left behind.
The chancellor will also announce its intention to increase the number of people who can access science and technology courses and spend about £30m on encouraging big business to mentor small firms.
The Conservatives will also announce plans to stop restaurant chains taking tips left for staff by diners.
Rebecca Long Bailey, Labour’s shadow business secretary, said: “This is now the fourth policy the Tories have copied from us at their conference.
“It’s beginning to feel like Groundhog Day.”