Talks on Britain leaving the European Union began Monday with both sides saying they will focus first on an orderly withdrawal: a deal for citizens living in each other's territory, border arrangements between Ireland and the United Kingdom and the amount that Britain will pay to get out of previous EU commitments.
United Kingdom negotiator David Davis and the EU's Barnier have one key issue over the first weeks of talks: building trust after months of haggling over leaks and figures over the final bill that Britain would have to pay for leaving.
For many Brexit advocates, those conditions would be impossible to accept as last year's referendum campaign focused on getting back control over laws and immigration from the EU.
Mr Davis said that while there was a long way to go - a conclusion is due by March 2019 - the negotiating teams had got off to a "promising start; we have taken the first, critical steps together".
May's government said it was "confident it can achieve a bold and ambitious deal that will work in the interest of the whole U.K".
'We must first tackle the uncertainties caused by Brexit, first for citizens but also for the beneficiaries of European Union policies and for the impact on borders, in particular Ireland'. Those issues are Britain's exit bill, estimated by Brussels at around 100 billion euros ($112 billion), the rights of three million European Union nationals living in Britain and one million Britons on the continent, and the status of the border between Northern Ireland and Ireland.More news: US calls on Arab states to ease Qatar blockade as crisis deepens
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"In the first step we will deal with the most pressing issues".
"We launch negotiations in a positive and constructive tone, determined to build a strong and special partnership between ourselves and our European allies and friends in the future".
The head of the biggest group in the European Parliament says that what Britain wants out of the Brexit talks is a mystery as negotiations get underway.
He also confirmed that Britain would opt for a "hard Brexit" that involves quitting the EU's single market and customs union, rejecting suggestions that after a poor election performance by May the line might be softened.
Over the next two years, the two sides will thrash out key issues surrounding Britain's leave, including citizens' rights, Britain's "exit bill" and the Irish border.
May was hoping to increase her support in the British election on June 8, but instead her party lost its outright majority and now has to try to form a workable government with a tiny party from Northern Ireland. The leaders are also likely to shape more clarity on the UK-EU relationship post the exit and the nature of trade deals between them. Finance minister Philip Hammond confirmed June 18 that it was still the plan to quit not only the EU but the customs union and single market as well. Business leaders have already warned against such a "cliff edge" scenario and are eager to see a transitional period to give them time to adjust after the split.