Asked about the potential impact of the government failing to secure a Brexit deal, he said: "If we move to WTO (World Trade Organisation) rules that would definitely require customs declarations and so it would be similar types of costs". But it also risks causing more domestic trouble for May, who needs to keep her divided Cabinet together and the Northern Irish party that props up her government onside.
Over a quarter of recipients said the UK's Brexit vote made them more inclined to vote for a united Ireland.
It also said it would keep Northern Ireland inside the European Union customs area.
The U.K. has been told to come up with a so-called "backstop" solution for the Irish border as part of its divorce deal with the European Union so that no policed frontier emerges on the island after Brexit.
And former Ukip leader Nigel Farage said: "Barnier is trying to break up the United Kingdom".
Britain may hope that this wording might still win approval from officials in Brussels, and May's spokeswoman said it was a "matter for the negotiations" as to whether the date became part of a legal text for Britain's withdrawal.
The backstop solution at the heart of the Brexit talks is due to snap into place to avoid a hard Irish border should an adequate free trade deal or technological answer not be in place by the end of the transition period at the end of 2020.More news: Teams begin to arrive for the World Cup
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"We are just feeling responsible for what we promised in December in our joint report that you will propose the first two options and then, in case there is no option from your side, then we have to be prepared that the Irish border is safe". That means no border posts or customs checks after Brexit to protect economic links and the hard-won peace on the island of Ireland.
Yesterday's agreement is created to provide a "backstop" - a guarantee of no hard border in Northern Ireland should other solutions fail.
The development came as Mrs May braced herself for possible defeat in the Commons next week on an amendment which would require her to try to negotiate a permanent customs union with the remaining EU.
"We could be in real crisis with no deal, which emphasises the importance of having a vote on the final package with the option of remaining in the European Union".
It also says the parliament must vote on the deal and agree to a referendum, a different kind of people's vote campaign must be fought without the past mistakes in 2019 and it must be held before March 29, 2019 to decide the country's future.
May's government is divided over two alternatives regarding which customs arrangement to seek with the European Union after the end of a transitional period created to bridge Britain out of the bloc, which ends in 2020.