Facing defeat because of opposition from dozens of pro-Brexit MPs, the government agreed to changes, including a clause to toughen conditions over customs arrangements and another to ensure the United Kingdom is out of the EU's Value-Added Tax system.
We will continue to argue, alongside our United Kingdom colleagues, that it is in the best interests of both United Kingdom and EU citizens and businesses to permit and facilitate trans-European and transnational legal services and to maintain access for lawyers to practise and establish within the EU through the Lawyers' Services Directive and Lawyers' Establishment Directive, or equivalent mechanisms.
"Once this thing has been started by a referendum, it can frankly only be finished by a fresh vote", Blair said.
Where the government might struggle is explaining its acceptance of the demand that the European Union must collect tariffs on Britain's behalf, if London is to do the same - a suggestion one expert said the bloc's negotiators were unlikely to accept.
Government whips overcame the rebellion by a dozen Tory lawmakers - reportedly issuing last-ditch threats it would prompt a no-confidence vote in the prime minister - by just seven votes.
"We saw yesterday there is no majority for May's Chequers' agreement".
But even before the European Union has had time to assess her vision for Britain's future ties with the bloc, her plans have come under fire from both camps in the Conservative Party.
One of the amendments would enshrine in law that there would be no customs border down the Irish Sea between the island of Ireland and the British mainland.
MPs are due to rise for the summer recess on July 24 but a motion tabled on Monday night would see the Commons rise on Thursday, with a vote pencilled in for Tuesday evening.
Two top pro-Brexit ministers, Boris Johnson and David Davis, quit in protest last week, while a string of junior walkouts have followed suit, including two more officials on Monday.
Theresa May's former Education Secretary Justine Greening earlier demanded that United Kingdom citizens be given the choice to remain in the European Union in a second Referendum.
By prevailing in Tuesday's vote, she avoided for now the prospect of having to go back on her word that Britain will not be part of any customs union after leaving the EU - something that would have enraged the pro-Brexit wing of her party.
Greening branded May's plan as "a fudge I can't support. There is not going to be a second referendum... under any circumstances", the spokesman told reporters. Downing Street and Buckingham Palace said Mr Trump's tour of Windsor Castle was not a state visit and the only plan drawn up involved the Queen greeting the president and his wife Melania alone.
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