BERLIN — Britain and the European Union began formal negotiations on Monday over how Britain will leave the bloc and what might come afterward. The talks began a year after British voters chose withdrawal in a referendum and three months after Britain gave formal notice of its intention to pull out.

The negotiations, which could last nearly two years, did not produce anything revelatory on the first day. But they are crucial to the future of Britain and to the cohesion of the other 27 member states of the bloc.

And they come at a time when the government of Prime Minister Theresa May is hanging by a thread, and when a new debate is in progress over what Britain’s future relationship with Europe ought to be.

The meeting, held around a large oval table, will be the first of many as the clock ticks toward March 29, 2019, the day when Britain will be out of the European Union, with or without a deal.