* Third round of Brexit talks run on Monday-Thursday in Brussels
* Britain wants more focus on future relationship with EU
* Bloc insists on settling chief divorce matters first
BRUSSELS, Aug 28 (Reuters) - British officials arrive in Brussels on Monday to push the EU towards talks about their post-Brexit ties, which the bloc refuses to do without an agreement first on London's exit bill and other divorce issues.
A third round of Brexit talks takes place more than a year after Britons voted in a referendum to leave the European Union, delivering an unprecedented blow to the post-World War Two European integration.
Chief Brexit negotiators, the EU's Michel Barnier and Britain's David Davis, will meet at 1500 GMT before more talks on Tuesday and Wednesday convene on technical level on expatriate rights, divorce bill and "other separation issues".
Senior officials will also tackle the conundrum of the future border between EU state Ireland and the United Kingdom's Northern Ireland, and a news conference is due on Thursday, according to a schedule published by Brussels.
Britain will present in detail its several papers released last week on issues ranging from customs arrangements to data sharing. They have often ventured out into the future relationship between London and what will become a 27-state EU.
Britain will be urging the bloc to show "imagination" and focus discussion on these future ties rather than just on the divorce settlement.
On Sunday, the opposition Labour Party said it would keep Britain in the European single market and customs union for a transitional period after Brexit, offering a clear alternative to the policies of Prime Minister Theresa May.
The bloc wants to settle chief separation aspects first and has already signalled the slow progress so far means jumpstarting talks about a new accord with Britain is now less likely in October, as had been expected.
"Both the UK and the EU have an interest to move forward quickly in negotiations and that requires us to make sufficient progress on citizens' rights, on the financial settlement on Ireland," said a senior EU official involved in the talks.
"The divorce issues should be relatively straightforward to sort out. So it is not a matter of time needed in terms of the technical complexity, it is a matter of political will."
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 Irish issue, extremely delicate because of the violent history between the two communities there, is fraught with economic consequences and politically complex.
On money, the EU and Britain seem to be seas apart on agreeing how much London should pay the bloc on departure to account for previous commitments.
Sides expect no major leaps forward this week in the talks aimed at unravelling more than 40 years of union.
But both highlight that time is scarce as the negotiations should conclude well before the provisional Brexit date of March 2019 to leave time for ratification and approval procedures of any deal by Britain, EU states and the bloc's parliament. (Reporting by Gabriela Baczynska and Philip Blenkinsop, editing by David Evans)