Previously, the United Kingdom had insisted on so-called parallel talks, in which both divorce terms and a future relationship would be covered simultaneously.
"As Brexit talks begin, it's important the voice of universities is heard clearly in the negotiations", Universities UK president and University of Kent vice-chancellor Dame Julia Goodfellow said.
"We are also clear that any trade deals forged outside the European Union must include measures to protect British producers and consumers from imports produced to lower standards". And our promise to you is that we will always strive to provide indispensable journalism to our community.
But the Brussels chief negotiator also made clear he was not planning on giving ground to Britain.
"In the first phase, the negotiation rounds will be broken down into three groups: citizens' rights, the single financial settlement, and other separation issues".
Britain now appears to have given in on the EU's insistence that the negotiations first focus on three key divorce issues, before moving on to the future EU-UK relationship and a possible trade deal.
The aim is to make sufficient progress to get leaders of the other 27 European Union countries to agree to move on to talks on a future relationship with Britain, including a trade deal, he said.
There are widespread questions over whether Britain may soften its Brexit goals outlined before the election, which include taking the United Kingdom out of the EU's single market for goods and services and the bloc's customs union. For the officials sitting down on Monday, at least on the European Union side, a major worry is Britain crashing out into a limbo, with no deal.
"I think the whole process will lead to a happy resolution which can be done with honour and profit to both sides", Johnson said as he went into a separate meeting of EU Foreign Ministers in Luxembourg.
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"The best way we can spend this week is to rebuild trust", rather than tackle the big hard issues right at the start, a European source said. A snap election early this month, in which Prime Minister Theresa May lost her majority, only added to the problems.
"I hope that today we can identify priorities and a timetable to allow me to report to (EU leaders) later this week (that) we had a constructive opening of negotiations".
"If we are going to radically change the way we work together, we need to get there via a slope not via a cliff edge", he told BBC television on Sunday.
Brexit Secretary David Davis and European Union chief negotiator Michel Barnier said discussions would be split into three stages: citizen rights, the single financial settlement and other separation issues.
A detailed paper will then be published on Monday, Mr Davis confirmed.
May herself will also have a chance to update the other 27 European Union leaders on her Brexit plans at a summit meeting in Brussels on Thursday.
With a further million British expatriates in the EU, May too wants a deal on citizens' rights, though the two sides are some way apart.
Mr Barnier quoted the founder of the trading bloc that later became the EU, Jean Monnet, as saying: "I am neither optimistic nor pessimistic".
"The pessimist see difficulty in every opportunity, the optimist sees opportunity in every difficulty".
"In a first step, we will deal with the most pressing issues".