The paper also alerts pharmaceutical companies to the fact that the testing of European medicines could no longer to be carried out in the United Kingdom in the case of a no-deal Brexit and it informs that the United Kingdom would have to be removed from EU databases.
He urged the Prime Minister to change course in his resignation statement in Parliament.
It is the latest blow for Mrs May who was yesterday roundly criticised in the House of Commons by departing foreign secretary Boris Johnson. Britons should be "great independent actors" on the world stage, not "rule takers", he said.
She said that a transitional arrangement for 21 months after March was not ratified "and therefore we must prepare for all scenarios, including the possibility of a "no deal" or "hard" Brexit". It said it objected to the amendment because it requires the government to take "all necessary steps" to join, while the government wants to join only if it can negotiate reasonable terms. Will the United Kingdom position change again in a few days or a week's time?
In his first detailed response to the White Paper, Mr Barnier noted that it was "the result of a very intense internal debate in the United Kingdom, a debate that was necessary and I think we have all seen that this debate in the United Kingdom is not over yet".
An EU diplomat said they were "really happy" to have the Chequers plan on the table, but said questions remain about the feasibility of key proposals on customs and a single market for goods.
Brexit-supporting MPs also successfully forced the government to enshrine in law that the United Kingdom will not accept any deal involving a separate customs arrangement for Northern Ireland to the rest of the UK.
Boris Johnson, the face of the Brexit referendum who resigned as foreign secretary in protest at Theresa May's proposal for leaving the European Union, warned her government must reverse course to seize the last chance for a clean exit from Europe.
Johnson said he was fully supportive of Prime Minister Theresa May in January 2017 when she laid out in an ambitious speech a desire to strike the right deal for Britain with the European Union after a majority of the public supported the break in a referendum months earlier.
Shouts rang out across the Commons.
In order to boost support for her Brexit stance, Mrs May is to hold a series of meetings with grass roots Tories over the summer, according to reports.
Even Davis jumped into the bad-tempered exchanges, asking May to publish the legal draft of a free trade treaty.
"It as though a fog of self-doubt has descended", Johnson said.
Eurosceptics can't say they weren't warned about how the Government's Brexit policy might change after Lancaster House.
Britain has said it and the European Union should act to ensure that cross-border financial contracts like derivatives and insurance policies can still be serviced after March, but the European Union reiterated on Thursday that it won't legislate for now. "Not the democratic disaster of ongoing harmonization with no way out and no say for the UK".
"We must try now because we will not get a chance again".
Sir Graham Brady, chairman of the backbench 1922 Committee, needs to receive letters from 48 Tory MPs before Mrs May can face a vote of no confidence.
A Tory MP has called for a vote of no confidence in the Prime Minister in a letter to his constituents.