The European Union says after a first day of talks on Britain's exit from the 28-member bloc that the clock is ticking on negotiations, but British Brexit minister David Davis said he's optimistic they will yield a swift and good outcome.
The two men will meet for a week every month to negotiate, and use the time in between to "work on proposals".
Davis's agreement to Monday's agenda led some European Union officials to believe that May's government may at last coming around to Brussels' view of how negotiations should be run.
In a two-day summit whose agenda is formally dominated by immigration, security and the economy, Mrs May will also brief her counterparts on the UK's commitment to a new £75 million plan created to stem the flow of illegal migrants from Africa to Europe.
The EU wants to discuss exit terms including the discussion on the exit fee before any discussion on trade.
Fiona Godfrey, Luxembourg-based spokesperson for British in Europe, added: "We and the three million European Union citizens in the United Kingdom must not be used as bargaining chips or for political point-scoring".
Market reaction was for the GBP to fall slightly against the Euro and the Dollars on the initial announcement on how the first day of talks was finalized, however since then it has relatively recovered.
Mr Barnier did not give a figure for how much the European Union will be demanding to settle the UK's outstanding budget commitments.
Davis, however, insisted the compromise was still in tune with his government's "hard Brexit" strategy. "In a first step, we will deal with the most pressing issues", Barnier said.
The document released after the first day of discussion on "Terms of Reference for the Article 50 TEU negotiations" stated: "The following initial negotiating groups have been established: Citizens' rights; Financial Settlement; Other Separation issues". There's a long way to go but we're off to a promising start.
The Sun, which backed May's center-right Conservatives in a June 8 election that cost her her parliamentary majority, also noted Davis had gone along with Brussels' plans after saying he would make getting immediate trade talks "the fight of the summer".
The two chief negotiators, Michel Barnier of the European Union and David Davis from Britain, immediately set off to find common ground in their working relationship, an important touchstone to see how amicable the biggest political divorce in decades will become.
She should, Soros said, seek to keep Britain in the EU's single market as Britain tried to extract itself.
"It's not how it starts, it's how it finishes that matters".
"I'm not in a frame of mind to make concessions", Mr Barnier told reporters in Brussels.
Mr Barnier warned the United Kingdom that it will have to pay a "substantial consequence" for its decision to leave the bloc. "It's not about punishment, it is not about revenge", Barnier said.
"So we have got a very sensitive political context, a very clear objective which is to preserve all the dimensions of the Good Friday Agreement and we have an bad lot of work to do - bilaterally, and also in coordination with the Dublin government on my side, so that we come up with imaginative and concrete solutions along the lines I have described, particularly taking into account the single market".