
Trade secretary Liam Fox told friends that her proposal "would make life very hard for me", according to a Mail report, because it would limit the UK's ability to strike new free trade deals outside the EU.
Blair, a prominent voice opposed to Brexit, resigned as prime minister in 2008.
EU chief negotiator Michel Barnier said Wednesday (10 October) that the withdrawal agreement between the EU and United Kingdom is "within reach" if London agrees to keep either Northern Ireland or the entire United Kingdom in the bloc's customs union before a separate deal on future relations is reached.
Theresa May is under pressure to reverse course after Cabinet ministers threatened to walk out over her reported plans for a potential Brexit "backstop" which could effectively keep Britain permanently inside a Customs Union with the EU after Brexit.
It would also send a message to business nervous about the process that the region remained "open for business", she added.
May has ruled out any agreement which could see customs or regulatory barriers being erected between Northern Ireland and mainland Britain.
His constituency contains the port of Larne, identified by European Union chief Brexit negotiator Michel Barnier as a place where checks on animals and animal products from Great Britain into Northern Ireland could be intensified in order to prevent a hard border with the Republic of Ireland.
More news: Sevastova to face Wozniacki in Beijing title clashWhy would a Unionist politician want to bring down a Conservative and Unionist government, lose the influence it has on that administration and risk the extra funding for Northern Ireland that the DUP received in exchange for agreeing to support the Tory minority government? "Indeed, Northern Ireland's access to any new United Kingdom trade deals would also be regulated by Brussels".
May's Brexit plan is unpopular with the public and the majority of the cabinet reportedly now prefer a free trade deal.
DUP leader Arlene Foster has insisted "these are significant days for Northern Ireland" as Brexit negotiations intensify.
Selmayr, secretary general of the European Commission, has been tasked with coordinating preparedness to protect the EU from economic and political damage if Britain leaves the bloc on March 29 next year without a divorce deal in place.
It comes as Brexit negotiations enter what is being referred to as a "tunnel phase", with no publication of the British or European Union position on the backstop to be published until it is agreed.
She said: "I am completely supportive of the prime minister". She needs to keep either her own party onside or attract votes from the main opposition Labour Party.
Labour demands that Britain retain "the exact same" perks it now has within the EU's customs union and single market - something May's so-called Chequers plan does not meet and which the EU rules out since London made a decision to leave both.