The note reads: "The UK is clear that the temporary customs arrangement, should it be needed, should be time limited, and that it will be only in place until the future customs arrangement can be introduced".
The so-called backstop proposal was published after last-minute wrangling over the wording with Brexit Secretary David Davis, who was reported to have been considering resigning unless it included a time limit.
The document also says the United Kingdom would be able to implement new trade deals - something which Brussels may push back against.
By that time other arrangements should be in place to prevent the need for the backstop, the document says.
The prime minister wants Britain to leave the EU customs union post-Brexit.
May's Conservative government is divided between ministers favoring a "hard Brexit", which would sever most ties with the EU and leave Britain free to strike its own trade deals around the world, and those who want to keep the United Kingdom closely aligned with the EU, Britain's biggest trading partner.
The EU has already been dismissing the United Kingdom blueprint, saying that a backstop can not be time-limited.
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Mr Barnier told a press conference in Brussels that it is not "feasible" to extend the backstop to the whole of the UK. "Our backstop can not be extended to the whole United Kingdom why because it has been designed for the specific situation of Northern Ireland", he said, adding that what was "feasible" for the relatively small territory of Northern Ireland was not necessarily feasible for all of the United Kingdom. The previously proposed annexation of Northern Ireland was totally unacceptable. "It would be the Hotel California scenario - we'd have checked out but we wouldn't have left". The UK needs to accept it.
But he said the EU's preferred option would work better and the United Kingdom could not take an "a la carte" approach to the European Union single market.
'I welcome the publication of the document, bu being very frank I think it raises more questions than it provides answer'.
Mr Barnier insisted that he is not discouraged and said that he will hold talks with David Davis on Monday to discuss the proposal.
Mr Davis threatened to quit yesterday after she initially did not put a date on her backstop plan. And he raised questions about whether the so-called backstop solution, created to avoid a border emerging if all else fails, can apply to the whole of the U.K. May wants it to, because the Northern Irish allies that prop up her government are demanding it. Does it respect the integrity of the single market/customs union?
I welcome publication of #UK proposal on customs aspects of IE/NI backstop.
'Michel Barnier has confirmed today that discussions will now continue on our proposal'.