This would be the case, even if the rest of the United Kingdom left the EU customs union, after ceasing to be a full member of the EU. European Chief Negotiator for the the EU, Michael Barnier, said that the document will be circulated among the 27 other EU nations and the European Parliament's Brexit steering group for revision and agreement before it is sent to the negotiation table.
He said a withdrawal agreement had now been produced with an Irish protocol which writes down in black and white how we can avoid a hard border on the island of Ireland.
May lashed out at the proposal to keep British-ruled Northern Ireland in a customs union if there is no better solution to avoid a hard border with EU-member Ireland.
The unionist letter said the vacuum created through the absence of devolved government in Northern Ireland, coupled with the ongoing negotiations on the UK's exit from the European Union was escalating tensions.
Brussels' chief negotiator Michel Barnier, presenting the EU's draft of an exit treaty for Britain, denied that the proposal, meant to avoid a disruptive EU-UK "hard border" on the island ofIreland, would loosen Northern Ireland's constitutional ties to the rest of the United Kingdom.
Opposition Labour leader Jeremy Corbyn raised the pressure on May on Monday when he said he backed the United Kingdom remaining in the customs union, a move that would largely solve the problem of keeping the Irish border invisible and make it easier for the United Kingdom to trade with the EU.
At a Brussels press conference, Mr Barnier signalled his frustration at the lack of progress in the negotiations, saying: "We must pick up the pace".
Mrs May has said her long-term goal is a "bespoke economic partnership", underpinned by a comprehensive free trade agreement guaranteeing tariff-free access to European Union markets for British goods and services.
Britain argues that it can avoid creating frontier checks in Ireland that could reignite sectarian conflict in the north by technological and administrative innovations for a "smart border" that would maintain "frictionless trade".
As prime minister, Blair was responsible for opening British doors to eastern European immigration as soon as Poland and other ex-communist states joined the EU in 2004 when Germany, France and other big economies exercised rights to hold off on granting them free entry for several more years.
Former Conservative premier John Major warned the government's promises were "just not credible", while his Labour successor Tony Blair said that Mrs May's hopes of keeping market access without following European Union rules was "not possible".
At their meeting in Number 10, Mr Tusk said "I'm not happy" with the Government's red lines, but told Mrs May: "After your decision on no customs union and no single market, it's some kind of breakthrough and we can start our substantive negotiations immediately".
The Prime Minister Theresa May has rejected the proposal. Tánaiste and Foreign Affairs Minister Simon Coveney says they haven't sprung any surprise on the British here.
"There can be no frictionless trade outside of the customs union and the Single Market", Tusk said.
Any hard border or a customs border in the Irish sea which would break up the UK's common market would be unacceptable, she added.