There have been faint signs of progress amid reports that the two sides are now working on a single text of a divorce agreement - rather than making counter-proposals.
Downing Street, which was given no...
But Mr Barnier's comments suggest there is still a long way to go before the crucial issues are settled.
She told reporters: "There can not be barriers to trade in the United Kingdom internal market". It says it will not tolerate the EU's suggestion of Northern Ireland staying in line with European Union customs rules to enable trade to flow freely across the border.
The Democratic Unionist Party has warned Theresa May that it could seek to remove her from office unless she walks away from a proposed Brexit compromise with Brussels to solve the Irish border question.
Following a meeting in Brussels with the EU's chief Brexit negotiator, DUP leader Arlene Foster dismissed suggestions that she was ready to soften her position, and said her party would not accept any new regulatory checks on goods crossing the Irish Sea.
The sabre-rattling came as Mrs May races against time to hammer out a divorce deal with Brussels.
How to prevent the return of a hard border, which some say could reignite sectarian divisions on the island of Ireland, has become one of the hardest hurdles to clear for both sides.
She claimed under the European Union position, there could be scores of checks on live animals and food products travelling within the UK.
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The joint survey by the University of Edinburgh and Cardiff University found that 87 per cent of the overwhelmingly unionist advocates for leaving the European Union believe the collapse of the peace process is justifiable if Brexit is delivered.
A spokeswoman for the DUP told HuffPost UK: "The government know our red lines on this". He said customs declarations could be done online in advance.
The DUP issued the threat by briefing broadcasters.
Sources in the party - whose 10 MPs are propping up the PM in power - today upped the ante by threatening to vote down the Budget if the deal sees Northern Ireland and mainland Britain "treated differently".
For industrial goods, he said it could be done by "market surveillance authorities" in company premises but he added that checks on animals and animal-derived products would still have to take place on the border.
The EU's top civil servant Martin Selmayr is said to have led discussion of a document on the consequences of no-deal - which the bloc has apparently decided not to publish for fear of derailing negotiations.
Barnier told small business leaders that the talks were "continuing intensively this week, day and night, with the aim. of having a deal within reach, if we follow through to the end of this negotiations, on October 17".
'We are going to have to carry this deal on our own benches.