The European Court of Justice will no longer have jurisdiction in the United Kingdom but the United Kingdom courts will have to pay "due regard" to its rulings.
But its publication threw the Commons into chaos on Thursday, after Labour MPs complained they had not been given a copy of the paper before Brexit Secretary Dominic Raab stood up to present it.
Brexit secretary David Davis and foreign secretary Boris Johnson quit cabinet in protest over the proposals and Mrs May's Brexiteers are in open revolt as they try to kill off her Chequers plan - keeping in reserve the option of trying to depose her.
But it would keep European Union rules on goods to protect complex manufacturing supply chains, using technology to levy its own duties on UK-bound products from outside the bloc, while diverging on services.
The white paper says free movement will end when the United Kingdom leaves the EU.
"Being tied to European Union regulations and the European Union tying our hands when seeking to make new trade agreements will be the worst of all worlds", wrote the Mansfield MP, who voted remain in a constituency where more than 70 per cent of voters opted to leave.
"It delivers on the vote that people gave on Brexit, it delivers the fact that we will have an end to free movement, we will have an end to the jurisdiction of the European Court of Justice in the United Kingdom, we won't be sending vast contributions to the EU every year, we'll be out of the Common Agricultural Policy, out of the Common Fisheries Policy", she said.
It is not yet clear when this new system would come in force - meaning the implementation of trade deals involving goods could be delayed.
In the foreword to the 120-page document Mr Raab, who replaced Mr Davis on Monday, will say: 'It is a vision that respects the result of the referendum, and delivers a principled and practical Brexit'.
"For those that are either criticising or carping or whatever else, they need to come back with credible alternatives".
Amendments tabled to the customs bill threaten to undermine Theresa May's plan for future UK-EU relations. The UK has spoken of boosting the Commonwealth and forging a free trade pact with India after Brexit, but that will not be easy if Britain refuses to budge from its tough position on movement of people and visas. I helped take the EU Withdrawal Bill through the House of Commons and we have got that bill through the House of Commons and the House of Lords, so through all of Parliament. Market players will now focus not only on EU's response to the document but also on May's leadership and a possible no-confidence vote, after already skipping one shortly ago.
"If not, they too will be held to account".