The prime minister has urged her cabinet to accept they must abandon hopes of a unilateral power to end the backstop and push for a joint review mechanism with Brussels.
But Ms Leadsom told BBC Radio 5 Live: “The UK cannot be held against its will in a customs arrangement.
“It must be capable for the United Kingdom to decide to leave that customs arrangement and it cannot be something that the European Union can then hold us to.
“And, frankly, it’s because that would be to then fail to fulfil on the will of the people expressed in the referendum and I very much doubt that we would get it through parliament.”
At stake is the fear of pro-Brexit Tories that the UK risks being locked indefinitely into the EU customs union – unable to sign its own trade deals – unless it can end the backstop unilaterally.
Ms Leadsom also rejected the idea of an independent body to review if an alternative solution has been found to avoid Irish border checks – something currently dependent on untested technology.
However, she insisted she was not on the verge of resigning, saying: “I’m sticking in the government to make sure that’s where we get to in the end.”
The Commons leader also dismissed suggestions that she was expecting other ministers to quit, adding: “No I’m not. That was a great surprise to me that he [Jo Johnson] resigned.
Nevertheless, the cabinet fightback means the prime minister’s hopes of agreeing an outline deal with her cabinet as early as tomorrow appear to be fading.
Senior ministers are also demanding to see full legal advice on the power to be conceded over ending the backstop, after Ms May indicated only a legal summary would be made available.
Meanwhile, EU leaders have also warned that crucial obstacles remain over how to settle future disputes over the Irish border and also over fishing rights.
Crucially, they are believed to have rejected Britain’s proposal of independent arbitration over ending the backstop, insisting the European Court of Justice must make the decision.
If an outline deal is not agreed by the middle of this week, it is unlikely that an emergency summit to sign it off can be held in November – throwing back a final agreement until the middle of December.
That would leave the UK having to ramp off hugely-expensive no-deal preparations and in danger of being unable to pass all necessary legislation before Brexit day next March.
Damian Hinds, the education secretary, warned cabinet rebels that the EU would not accept the UK being able to end the backstop.
“If you have too hard a line about saying, 'well we must just have a totally unilateral exit, or there's an absolutely fixed, hard end date', that is very, very unlikely that is going to be negotiable with the other side,” he admitted.
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