It comes as the prime minister faces intensifying pressure from the Eurosceptic wing of her party to drop her Chequers agreement on the future UK-EU relationship – a plan that has already led to resignations of cabinet heavyweights Boris Johnson and David Davis.
The amendments were lodged today and Priti Patel, the former cabinet minister, has also signed the documents alongside Marcus Fysh, John Redwood, Bernard Jenkin and Craig McKinlay.
While it is highly unlikely Labour would support Mr Rees-Mogg and the hardline Brexiteers on the Tory backbenches it would be the first significant test of strength for Ms May’s Brexit critics.
One of the amendments if passed will prohibit the UK collecting tax or duties on behind of another territory “without reciprocity”. This would cause a serious headache for Downing Street as it would block the current proposal of a “facilitated customs arrangement” which aims to collect taxes after Brexit – on behalf of the EU – for goods passing through the UK en route to the continent.
A second amendment orders the government to commit itself in law not to allow a customs border down the Irish Sea. This has the support of the DUP MP Sammy Wilson.
Ms Patel told The Independent: “The British people need firm guarantees that when we leave the EU we will have the freedom to make our own trade deals and not be subject to any EU control or veto. Our future prosperity rests on us being a global beacon of free trade reaching out and securing trade deals with emerging and fast growing economies.
“The 17.4m people who voted to leave the EU and those who backed the Conservative manifesto expect Britain to have these freedoms and for there to be no future EU meddling in our trade policy and economy.”
Speaking to The Sun newspaper, Mr Rees-Mogg added: “Unfortunately Chequers was a breakdown in trust. Brexit meant Brexit, but now it appears Brexit means remaining subject to European laws. I believe this will help the government stick to the promises it made.
“It may resolve the dilemma the Prime Minister faces. Does she rely on Labour votes to achieve Brexit or does she change her mind and go back to Lancaster House. Will she stick to her earlier words?”
But Liam Fox, the international trade secretary, earlier told a Commons committee the Chequers plan was designed to be a “credible offer” to the EU in order to take the negotiations forward.
“We hope that they will respond positively to that,” he said.