BRUSSELS—The European Union’s chief Brexit negotiator warned Wednesday that there will be “serious consequences for everyone” if the two sides fail to clinch a deal within two years.

Michel Barnier, who will be leading the EU side during the Brexit discussions, said there could be “total uncertainty” for Britain if no deal is secured in that time frame.

He insisted that he will be negotiating in good faith to make sure that a mutually acceptable agreement is reached, telling an audience of lawmakers from parliaments across Europe that “this scenario of ‘no deal’ is not ours.”

Britain is slated to trigger the two-year period of its exit from the EU on March 29, with the talks starting for real in May.

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Barnier said no deal could leave four million European and British citizens uncertain about their rights and future, result in the reintroduction of strict customs rules, create air traffic chaos to and from Britain and lead to the suspension of exports of nuclear materials.

The former French government minister said the talks he will lead will be transparent and open, saying that “these negotiations cannot take place in secret.”

He said the first aim would be to end uncertainty for EU and British students and pensioners abroad, as well as health care workers in the U.K.

The EU’s watchword, he said, will be “citizens first.”

Barnier insisted that Britain will face no punishment for leaving, but that “we must settle the accounts. We will not ask the British to pay a single euro for something they have not agreed to as a member.”

Some estimated suggest the EU wants Britain to pay a hefty divorce bill of up to 60 billion euros ($64 billion), to cover EU staff pensions and other expenses the U.K. has committed to. Britain hasn’t ruled out paying, but is expected to contest the bill.

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