Downing Street says the letter sets out the prime minister's commitment "to never accepting any circumstances in which the United Kingdom is divided into two customs territories".
The country would then be able to negotiate with Brussels as a "third country" for two years, making it easier to agree on a new free trade deal and avoid having to pay the full 38 billion pounds ($49 billion) divorce bill.
The letter is seen by some observers, as well as the DUP, as part of a laying of the groundwork by the prime minister for a showdown with the party over checks in British ports, or factories in Northern Ireland or Great Britain.
The prime minister's letter has provoked the ire of DUP leader, Arlene Foster, claiming May's words have set off "alarm bells" for her party on the issues of the customs union and single market.
In the five-page letter to Arlene Foster, the DUP leader, and Nigel Dodds, her deputy, Mrs May said the European Union is still pushing for the "backstop to the backstop" but insists that she would never allow a divide between Ulster and Great Britain to "come into force".
A Downing Street spokesman said the prime minister would not agree to "anything that brings about a hard border on the island of Ireland".
Walker said he did not think a disorderly Brexit was likely, but he added that if it did come to that the rights of European Union citizens in Britain would be protected.
He told BBC Radio 4's Today programme that the letter "makes it quite clear the Government has accepted there will be a Northern Ireland-only backstop, that that backstop will require specific alignment for regulations" without Northern Ireland being given a say.
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Police say at least 10 people are known to have been injured and others are self-reporting with injuries at local hospitals. There was no screaming, she said. "I think everyone was in so much of a shock that it was sheer panic", Whittler said.
Downing Street reiterated the PM's own commitment to avoiding a hard border.
The row comes as Brexit is expected to dominate the agenda of the British Irish Council, which will be attended by the taoiseach, Leo Varadkar, David Lidington, who is in effect May's deputy, and the Northern Ireland secretary, Karen Bradley.
"And I think if we do that, if we listen to the voice of Northern Ireland as a whole that will help us to come to an agreement".
The DUP said it is "totally unacceptable that there could be a Withdrawal Agreement which provided that Northern Ireland at any time in the future could be subject to the rules of the Customs Union or parts of the Single Market whilst the rest of the United Kingdom was not".
Wilson said: "She is now contemplating signing up to a legal agreement which, regardless to her aspirations, would be binding on the government of the UK".
"I hope and I believe that we can secure that majority in Parliament for the agreement".
"There is no clean break here, Brexit is going to go on for a very long time".