While May has repeatedly said she wants a special and deep partnership with the club Britain joined in 1973, she has also laced her assurances with threats that a breakdown of talks could harm security cooperation.
Barnier speaks of a willingness to look at various options but EU officials also stress that greater access to EU markets will mean accepting greater costs, closer to EU membership, and question whether Britain can find a political consensus on that.
"We're not going to get into - and I know there has been a lot of talk about our position in relation to social issues for example - those are matters for the Northern Ireland assembly - they are not matters for Westminster and therefore we will not be dealing with them at Westminster", she told the BBC.
"As we set out in the Article 50 letter, our view is that withdrawal agreement and terms of the future relationship must be agreed alongside each other", a spokesman for Britain's Brexit ministry said.
And as leaders welcomed the new tone in London and talk of a "softer Brexit" that may be less disruptive than May's clean break with the single market and customs union, officials from at least some governments saw compromise on the British bill.
The EU says Britain must honour its contributions to the bloc's budget, which has already been agreed up to 2020, as well as commitments to development programmes for poorer member states.
May's strategy was thrown into confusion by last week's election in which she squandered her Conservative Party's parliamentary majority. "We believe that the withdrawal process can not be concluded without the future relationship also being taken into account".
"We believe that the withdrawal process can not be concluded without the future relationship also being taken into account", the spokesman said.
"We want to see a Brexit that works for everybody, not just for Northern Ireland", she said.
There are also differences over the other priority issue for Brussels - securing the rights of 3 million European Union citizens living in Britain - but diplomats see those as less problematic.
In Luxembourg, Britain's finance minister said that protecting jobs and the economy should be the main focus in upcoming discussions.
"We're ready on the European side".
Speaking as he arrived for a meeting of European Union finance ministers in Luxembourg, he said: "As we go into that negotiation, my clear view - and I believe the view of the majority of people in Britain - is that we should prioritise protecting jobs, protecting economic growth and protecting prosperity as we enter those negotiations and take them forward".
London fire: 58 missing presumed dead Protesters sit down in Oxford Circus during a rally calling for justice for those affected by the Grenfell Tower fire on June 16. Condoling the incident earlier, Londor Mayor Sadiq Khan said, "The bad news, I'm afraid, is lots of people died in the fire".
Trump Appears to Confirm He Is Under Federal Investigation
In a series of tweets on Friday morning the president confirmed that he was being investigated for firing James Comey on May 9th. In a tweet , Trump appeared to confirm that that he was being investigated for firing ex-FBI director James Comey .
Watertown Sailor Dead In Destroyer, Container Ship Collison
The deceased sailors are: Dakota Kyle Rigsby, 19, of Palmyra, Virginia; Shingo Alexander Douglass, 25, of San Diego; Ngoc T. Most of the more than 200 sailors aboard would have been asleep in their berths at the time of the pre-dawn crash.
'Significant progress' in Theresa May's talks with the DUP Foster and Prime Minister Theresa May may work together after Tories failed to win an overall majority in the UK General Election .
Ruddy: Mueller Appears 'Out to Get the President' His spokeswoman Sarah Huckabee Sanders, however, would later tell reporters the president "has no intention" to dismiss Mueller. Donald Trump is in way over his head, and his presidency looks like it is living on borrowed time.
Death toll from London inferno rises to 58 Hundreds have been left homeless, putting more pressure on officials in a city plagued by a chronic housing shortage. The fire at the 24-story building has led to community anger and protests over the British government's response.
Trump confirms he is being investigated over Comey firing in tweet
Trump's tweet deepens the potential conflict by asserting that Comey's firing was Rosenstein's idea, Feldman says. In a later tweet, the president seemed to confirm he is under investigation for possible obstruction of justice .
Galantino, segretario Cei: "Ius Soli tema importante, basta gazzarre ignobli in aula" La legge sullo ius soli garantirebbe più sicurezza? La legge sullo Ius Soli è una follia contro la quale ci opporremo. Queste le parole del segretario generale della Cei, parlando alla Repubblica delle Idee a Bologna.
British PM May tries to quell public anger after deadly London fire Hundreds have been left homeless by the blaze, putting more pressure on officials in a city plagued by a chronic housing shortage. The tragedy has provoked a enormous response from nearby communities that have donated food and shelter to the victim.
Uncertainty over Islamic State leader's fate after airstrike
ISIS militants have nearly been defeated in the two acclaimed territorial capitals of the group in Syria and Iraq. Both are still under attack by various groups fighting under the cover of air strikes by the US-led coalition.
58 missing, presumed dead in London high-rise fire Adding: "When we were looking at this when I was DPP in relation to other fires, we were looking at manslaughter charges". The British government has announced a 5 million-pound ($6.3 million) emergency fund for the victims.
New Zealand beat England in IRB World U20 Championship final
Incredibly, it was a front-row player who was the star of the final as Asafo Aumuma scored a hat-trick from the hooker position. New Zealand coach Craig Philpott says it is disappointing Falcon won't be able to play in the final.
Donald Trump 'yells at TVs in the White House' about Russian Federation investigation Representative Adam Schiff has said Trump and his legal team seem determined to "take down" Special Counsel Robert Mueller . And, short of firing Mueller - which would be political suicide for Trump - he just has to wait and see how it plays out.
Missing: The desperate hunt for lost relatives after London tower block fire "His dream was to be able to go back home one day and rebuild Syria". May has pledged to hold a public inquiry into the fire.
Vaccini obbligatori, più ne salti e più paghi di multa
Di queste ne abbiamo individuate 4 o 5 non propriamente di richiesta di informazione, ma chiaramente provocatorie. Ovviamente, la violazione dell'obbligo vaccinale comporta l'applicazione di significative sanzioni pecuniarie.