* Third round of Brexit negotiations opens
* Britain wants talks about post-Brexit relationship
* Bloc wants to solve chief divorce matters first (Recasts with Barnier and Davis, adds EU official)
BRUSSELS, Aug 28 (Reuters) - The European Union's chief negotiator Michel Barnier said on Monday he was concerned at the slow progress of Brexit talks, while his British counterpart David Davis called for "imagination and flexibility" to move on.
British officials arrived in Brussels on Monday hoping to push the EU towards talks about their post-Brexit ties, which the bloc refuses to launch until there is agreement on London's exit bill and other "divorce" matters.
"To be honest, I am concerned. Time passes quickly," Barnier said in short comments offered jointly by the two men to the media.
"We must start negotiating seriously ... the sooner we remove the ambiguity, the sooner we will be in a position to discuss on the future relationship and a transitional period."
The two sides hold a third round of Brexit talks from Monday to Thursday. It comes after Britain last week made public its positions on issues ranging from customs rules to data sharing.
The position papers often touch on the future relationship between London and the EU, as London wants to focus discussion on these future ties rather than on just the divorce.
"The UK government has published a large number of papers covering important issues related to our withdrawal and our vision for a deep and special partnership," Davis said.
"We want to lock in the points where we agree, unpick the areas where we disagree and make further progress on the whole range of issues," he added.
To do that would require "flexibility and imagination from both sides".
But the EU wants to settle the major separation issues of ensuring expatriate rights, agreeing a divorce bill and squaring the circle of the future Irish border before jumping into talks about post-Brexit ties with London.
"The EU 27 and the European Parliament are united. They will not accept that separation issues are not addressed properly," Barnier said. "I am ready to intensify negotiations over the coming weeks in order to advance."
NO BREAKTHROUGH EXPECTED
The EU has already signalled that the slow progress so far has made talks about a new accord with Britain less likely to start in October, as had been originally expected.
After Barnier and Davis sit down on Monday, more technical talks will follow on Tuesday and Wednesday to tackle expatriate rights, the divorce bill and "other separation issues".
While there is some convergence on safeguarding the rights of EU citizens residing in Britain and Britons living on the continent, more technical work is needed, EU sources say.
The EU and Britain seem far apart on agreeing how much London should pay the bloc on departure to account for previous commitments.
The Irish issue is extremely delicate because of the history of political violence there, as well as the complex economic consequences of Brexit.
Dublin said on Monday much of the future border arrangements between Northern Ireland and Ireland could be solved before Brexit talks enter the next phase.
Neither side expects major breakthroughs this week in talks aimed at unravelling more than 40 years of union. Neither seems ready for major political concessions, as highlighted by the fact that Davis was planning to return to London almost immediately after the meeting with Barnier.
Still, both Britain and the EU stress that time is scarce. The talks should conclude well before the provisional Brexit date of March 2019 to leave time for approval of any deal by Britain, EU states and the bloc's parliament.
An EU official welcomed the fact Britain had presented its papers, but said it was "clearly worrying that we have major differences of core issues ... with very little time to land all this, even if Britain moves."
Britain's opposition Labour Party on Sunday offered an alternative to the policy pursued by Prime Minister Theresa May by saying it would stay in the European single market and customs union for a transitional period after Brexit.
The British and German chambers of commerce together urged negotiators on Monday to start talks about future trading relations, and particularly customs arrangements, swiftly.
Barnier said on Monday the EU and Britain had to remain allies in combating terrorism, cyberattacks and information wars.
"The fact remains that the Union of 27 and the United Kingdom will have to join forces to stand up to common threats: the security of our citizens cannot be haggled over," he wrote in the French daily le Monde. (Additional reporting by Philip Blenkinsop and Jan Strupczewski; editing by Andrew Roche)