Irish Prime Minister Leo Varadkar pushed Theresa May for specifics on the issue of the non-physical border between Ireland and Northern Ireland following the Brexit.
The passing of the bill, which largely seeks to copy and paste EU law into British legislation, is especially important for a government that is being scrutinised over its faltering Brexit strategy.
The EU's chief Brexit negotiator Michel Barnier said that the UK and EU had made no breakthroughs in the third round of Brexit talks.
The negotiations are dealing with issues around Britain's divorce – Britain's exit bill, the rights of EU citizens living in Britain, and the Northern Ireland border.
The European Union and Britain have little less than two years to decide the terms before the divorce. British PM Theresa May's cabinet appears bitterly divided over the type of outcome it wants from the talks.
Brexit Secretary David Davis arrives in Brussels on Monday to launch talks he hoped would produce a "new, deep and special partnership" with the EU in the interest of Britons and all Europeans.
Here are some of the problems facing the British prime minister as she attempts to come to grips with a disappointing election result.
The prime minister is currently facing calls to resign after losing a parliamentary majority in a snap election. However May is forging ahead with forming a new government, saying Britain needs "certainty" to leave the European Union.
One of the biggest challenges of Brexit will be London's exit bill. The negotiations are set to start after the British general election on June 8.
The future of Gibraltar, a rocky British outpost on Spain's southern tip, has become the first major dispute of the Brexit negotiations.
In a defeat for the government, peers voted 358-256 for an amendment requiring protection of the rights of more than three million European citizens after Britain leaves the bloc.
A majority of the MPs in the House of Commons backed a bill that allows Prime Minister Theresa May to initiate the process of pulling Britain out of the EU.
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