* Davis, Barnier launch week-long first round on Monday
* Negotiators will work in teams on key priorities
* Rights of expatriates and British "bill" on agenda
* EU looking for urgency, detail from London
By Alastair Macdonald
BRUSSELS, July 16 (Reuters) - Brexit Secretary David Davis launches a first round of negotiations on Britain's withdrawal from the European Union on Monday when he meets the EU's Michel Barnier for four days of talks between their teams in Brussels.
A month after a first meeting where the two exchanged gifts inspired by a shared passion for hillwalking and spoke of the mountain of complexity they must climb, the Frenchman will press Davis to agree to Britain covering substantial British financial commitments and offer more detail on other British proposals.
With little more than a year to settle divorce terms before Britain leaves, deal or no deal, on March 30, 2019, the 27 other EU national leaders want British Prime Minister Theresa May to rally her divided nation swiftly behind a clear, detailed plan that can minimise economic and social disruption across Europe as its second biggest economy cuts loose from the continent.
Davis and Barnier will shake hands for the cameras at the European Commission's Berlaymont headquarters at 9:15 a.m. (0715 GMT) before a first full session of talks. Negotiators will then break up into groups discussing four key areas of priorities before a planned news conference on Thursday afternoon.
Barnier, who secured Davis's consent last month to the EU's broad structure for talks, wants to hold the Englishman publicly to whatever else has been agreed during the week, EU officials say.
Working groups will focus on three areas: the rights of over 4 million people living as expatriates on either side of the new UK-EU frontier; the EU demand that Britain pays some 60 billion euros ($70 billion) to cover ongoing EU budget commitments; and other loose ends, such as what happens to British goods in EU shops on Brexit Day, or to outstanding EU court cases involving Britain.
A fourth set of talks, run by Davis and Barnier's deputies Oliver Robbins and Sabine Weyand, will focus on curbing problems in Northern Ireland once a new EU land border separates the British province from EU member Ireland. Some of that will have to wait for clarity on future trade relations.
BREXIT BILL
One key early advance that EU officials hope for this week is for Britain to stop challenging the principle it will owe Brussels money -- though how much will have to be argued over and cannot be calculated until Britain actually leaves.