"The compromise plan that we have from Chequers doesn't achieve any of those".
But the government was saved from humiliating defeat by three Labour MPs, Frank Field, Kate Hoey and Graham Stringer, voting with the Government and another dozen or so Labour MPs missing the vote for whatever reason.
To dispel the Tory infighting on Tuesday, May is expected to ask MPs to vote to start the parliament's summer recess on Thursday, five days before the expected end to the political season.
The ex-foreign secretary used a Daily Telegraph column to ominously say "I will resist - for now - the temptation to bang on about Brexit".
Pro-Europeans are also unhappy, including with the plan for loose ties with the European Union on Britain's dominant services sector, and former prime minister Tony Blair said it would lead to a "confused outcome".
Mrs May went down to defeat on a separate amendment to her flagship Trade Bill, which will require her to seek continued United Kingdom participation in the EU's system for regulation of medicines after Brexit.
MPs backed an amendment that would keep the United Kingdom in the European medicines regulatory network.
May's climbdown provoked a backlash from Remain-supporting Tories, who accused her of being "frightened" of her backbenchers and threatened their own rebellion when another piece of Brexit legislation is put to the vote Tuesday.
The spokesman said Mrs May was "very clear that the proposal we put forward at Chequers delivers on the will of the people in the referendum".
Mr Thomson said the prime minister had previously used major speeches to set out her views on what Brexit actually meant, what she was seeking to achieve and what her red lines were.
"We will be accepting these four amendments because we feel they are consistent with the white paper we published last week", a source told the Press Association.
Labour backs the idea of a customs union with the EU after Brexit - but the government says this would mean the United Kingdom is unable to strike its own global trade deals.
But the suggestion that MPs take extra time off during one of the most critical - and busiest - periods in recent parliamentary history has gone down badly.
He tweeted: "I can't possibly go along with that and I don't see how anyone else could at this critical time with the clock ticking on #Brexit; it would be shameful even to consider it".
"We can't rely on anything", said Warren East, CEO of United Kingdom engine maker Rolls Royce, who said his firm could start stockpiling parts soon if it looked like Britain was heading towards a disorderly exit from the EU.
But an early holiday would stymie Tory MPs plotting against the increasingly politically fragile premier.
In her reply, Mrs May told him: "I do not agree with your characterisation of the policy we agreed on at Cabinet on Friday".
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