Leading eurosceptics offered to compromise by agreeing to have EU officials based at UK ports to check cross-border cargos – if it paved the way for a looser free trade deal than the PM’s Chequers plan envisages.
Meanwhile, some pro-Brexit MPs have warned party whips not to rely on their support in key non-Brexit votes, in protest at Mrs May failing to take a tougher line with Brussels.
The developments come at a crucial time in Brexit talks.
The European Union is expected this Wednesday to formally respond to Mrs May’s Chequers proposals – key elements of which have already been shot down by eurocrats.
Next week, on October 17 and 18, comes a summit of EU leaders where many hope for a breakthrough.
Before then, the UK is due to publish new proposals on a Northern Ireland “backstop” – a plan to avoid creating a hard border with Ireland if a permanent solution is not found by Brexit day next March.
Britain is believed to be considering offering to keep the whole UK in the EU customs union for a certain time while letting Northern Ireland align more closely with single market rules.
Many Tory Brexiteers oppose Mrs May’s Chequers deal on grounds it enslaves the UK to EU goods trade rules and could impede Britain in making lucrative new trade deals around the world.
Some laid out concessions they said could enable an alternative free trade deal based on the EU’s with Canada.
Members of the European Research Group of Tory MPs said they would back basing EU officials at UK ports after Brexit – an idea suggested last month by EU negotiator Michel Barnier.
They would agree the UK enforcing EU rules on goods which British firms export to the Continent.
Both ideas are seen as ways to avoid a hard border with Ireland and keep trade free-flowing.
Group leader Jacob Rees-Mogg said he could support the two “sensible steps … to help to minimise friction in trade while allaying European concerns about compromising the single market”.
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Tory former leader Iain Duncan Smith said shared border checks could be modelled on the existing system where cross-Channel passport checks are done by French officials in Dover and UK officers in Calais.
Extending this “would enable the Republic of Ireland and the French authorities to make the customs and regulatory checks they need”, said Mr Duncan Smith, insisting the “half in, half out” Chequers deal neither delivered on the referendum vote nor worked for the EU.
Another senior Brexiteer commented: “It’s important to test the EU on this. No-one wants a hard border but solutions have to be found and are out there, as the ERG has already outlined.”
Separately, former Brexit Minister David Jones said the PM must stick to her red lines and rule out membership of a customs union, telling the Sun: “We must not be dancing to the tune of the EU.”
Meanwhile, some Tory Brexiteers are ready to flex their muscles in key non-Brexit parliamentary votes if Mrs May seeks to force a Chequers-type deal through the Commons with Labour support.
Senior MP Sir Bernard Jenkin messaged a group of fellow Tories: “Make no mistake a soft/non Brexit pushed by the Conservative establishment but put through with Labour support will look like we are abandoning our supporters and remove any sense of obligation among Conservative-Brexit supporting MPs to continue to support the Government.”
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Sir Bernard denied he was suggesting that he or any Conservative MP would do something as drastic as voting against the Government’s October 29 Budget.
But another rebel said: “She (Theresa may) hasn’t got a majority and by God, she’s going to be shown she hasn’t got a majority.”
Others have privately warned party whips not to rely on their support in votes but play down speculation about an organised Brexiteer plot to disrupt government business.
Looking ahead to next week’s EU summit, a Downing Street source said: “We have always said we are working hard for a deal this autumn. However, there remain big issues to work through, and as the Prime Minister has said this will require movement on the EU side.”
Former head of MI6 Sir Richard Dearlove, a known Brexit backer, told Sky News he was still “happy” to see Britain leave the bloc.
“I see it as an issue of sovereignty … It’s a natural point of divergence for us,” he said.
“I’m not underestimating the difficulties of leaving but I’m absolutely confident that we can survive and thrive outside a continental alliance but still be a major player in European geopolitics.”
Japan would welcome Britain “with open arms” into a major multi-country trade alliance, Prime Minister Shinzo Abe said.
He urged the UK to avoid a “disorderly Brexit” and told the Financial Times he hoped “the negative impact of Brexit to the global economy, including Japanese businesses, will be minimised”.
Brexiteers will be encouraged by his warm words about welcoming the UK into the Trans-Pacific Partnership of 11 countries including Japan, Vietnam, Malaysia, Canada, Mexico and Australia.
Experts have warned that staying too closely tied to the EU customs union will limit Britain’s ability to make new free trade deals by joining the TPP.
A DExEU spokesperson said: “We have set out a proposal for our future economic relationship based on a frictionless trade in goods.
“That is the best way to protect jobs here and in the EU and to avoid a hard border between Ireland and Northern Ireland, while respecting the referendum result and the integrity of the United Kingdom.
“We will continue to work at pace to conclude these negotiations in the autumn.”