Angry pro-Brexit Conservative lawmakers accused EU negotiators of wanting to land grab Northern Ireland and transform it into an exclave of the bloc - an accusation triggered by Brussels' defining a "backstop" arrangement for the Irish border whereby Northern Ireland would remain in the EU's customs union, abide by its regulations and laws allowing for tariff-free trade and free movement of people on the island on Ireland.
The plan for the Irish issue was dealt with in the draft exit deal that the EU Commission unveiled on Wednesday (28 February).
He said the UK Government's decision to rule out membership of the single market and customs union had been acknowledged "without enthusiasm and without satisfaction".
Rhetoric on both sides has turned sharper following the interim accord in December, with European Union officials urging May to give them a clear idea of what her deeply divided government wants on trade and for Northern Ireland with Brexit just 13 months away.
"Every party in Northern Ireland, Great Britain and the Irish Republic, along with both governments have said they wish to avoid a hard border".
European Union officials pointed out that the list of issues where rules between the Republic of Ireland and Northern Ireland would not be aligned is longer than that of where it would need to be harmonised.
The bank, which has large operations in both the Republic of Ireland and Northern Ireland, wants to know what sort of relationship there will be in their border once the United Kingdom officially leaves the European Union in March 2019.
The deputy prime minister, Simon Coveney, welcomed the UK's reiteration of its commitment to the Good Friday agreement, but said "these commitments now need to be translated into concrete proposals on how a hard border can be avoided".
On Northern Ireland the commission worked out the fallback option.
Blair told the BBC that he was hearing positive reactions on the continent: "Brexit may be bad for Britain; it's bad for Europe", he said.
"It's good that she seems to have taken the no-deal off the table, but it's not about a soft Brexit, it's about a workable Brexit", he said.
May's government is seeking more time, but because it has suggested no other date and because legally the period can not remain open-ended, the EU's preferred date is the one being used. Its stated intention, as a fallback should no other agreement be reached, is to "create a common regulatory area on the island of Ireland in order to safeguard North South cooperation, the all-island economy, and protect the 1998 [Good Friday] Agreement".
"At this point transitions is not a given", Barnier said.
May will reiterate the threat not to pay a divorce bill in meetings Thursday with Donald Tusk, president of the European Council, in which she will brief him on the outlines of a speech she is due to make Friday on what Britain wants in terms of a future trade deal with the EU.
In an apparent warning to hardline Brexiteers to temper their expectations, Mrs May used the high-profile address to acknowledge that neither side would get "exactly what we want" in talks on the future UK/EU relationship.
Meanwhile the European Union machinery moves on despite the political stalemate paralysing the negotiations.
Tony Blair, the former Labour prime minister who is among the more prominent campaigners trying to halt Brexit, was in Brussels on Thursday, aiming to persuade European Union policymakers to be ready to welcome Britain to remain if it changes its mind - and be ready to show a will to reform, especially to curb the easy migration across the European Union that anxious many Britons.
Those guidelines are then expected to be adopted on 23 March.