By Jenny Gross in London and Laurence Norman in Brussels 

The U.K. on Wednesday formally began the process of exiting from the European Union, starting on an unprecedented path from which British Prime Minister Theresa May said there would be no turning back.

Nine months after Britain voted to leave the EU, Tim Barrow, Britain's ambassador to the bloc, hand delivered a letter to European Council President Donald Tusk formally notifying the bloc that the U.K. will be the first country ever to leave it.

"This is an historic moment from which there can be no turning back," Mrs. May said in Parliament. "Britain is leaving the European Union."

Managing Britain's exit will be a major political test for Mrs. May, who has only a small majority in Parliament. She faces competing pressure from lawmakers on the right wing of her Conservative party who want a complete cutting of ties with Brussels and from politicians in Scotland, who say they will secede from the U.K. if Mrs. May fails to cut a deal that maintains close trade ties.

The negotiations will also be a test of the unity of the remaining 27 nations of the EU--which have different priorities--and the endurance of the bloc as a whole; the U.K.'s exit, and the shape of any new deal, will dramatically shift the internal dynamics of the bloc.

Striking a conciliatory tone, Mrs. May attempted to reach out broadly--offering assurances of good will to the bloc, to fellow Britons, however they voted, and to EU citizens who make the U.K. home. She promised to "represent every person in the United Kingdom--young and old, rich and poor, city, town, country and all the villages and hamlets in between."

"I choose to believe in Britain and that our best days lie ahead," she said, adding that "we will do all we can to help the European Union prosper and succeed."

Mr. Tusk, speaking in Brussels, expressed regret about Britain's decision to leave, saying that "in essence, this is about damage control."

"There is no reason to pretend that this is a happy day, neither in Brussels nor in London," he said. "We already miss you."

The triggering of Article 50 of the Lisbon Treaty, which governs EU law, opens a two-year window for Britain to negotiate the terms of its exit from the bloc, unraveling 44 years of ties.

Many of Britain's anti-EU politicians have been waiting for this moment for years. "The impossible dream is happening," said Nigel Farage, one of the leaders of the Brexit movement, in a message from his Twitter account. "Today we pass the point of no return."

The negotiations are expected to be tough. Early indications are that Britain and the EU are far apart. Mrs. May has said Britain would pursue a clean break from the EU, regaining control over immigration, leaving the jurisdiction of the bloc's courts and exiting its common market.

British officials have said they want to negotiate the best new deal they can for trade with the EU. European leaders have said they don't want to punish the U.K. for leaving, but won't grant Britain a better deal outside the club than it had in it.

Mrs. May acknowledged that in her speech, saying she accepted European warnings that Britain can choose what it would like to keep from the EU while dropping obligations it doesn't.

"We understand that there will be consequences for the U.K. of leaving the EU," she said. "We know that we will lose influence over the rules that affect the European economy. We know that U.K. companies that trade with the EU will have to align with rules agreed by institutions of which we are no longer a part, just as we do in other overseas markets. We accept that."

Mrs. May wants to negotiate the U.K.'s new trading and financial relationship with the 27 other EU member states, during which she will strive to protect London's status as a financial hub.

One of the first--and likely most contentious--issues in the negotiations is set to be how much the U.K. will have to pay to exit from the bloc. While some U.K. officials have said the country shouldn't have to pay anything, EU officials say the bill, which would include payments for programs the U.K. had committed to before it voted to leave, could be as high as EUR50 billion ($54 billion) to EUR60 billion.

Mrs. May said in the letter the U.K. wants talks on the future relationship with the EU to take place alongside negotiations over the terms of its exit, acknowledging that reaching a comprehensive deal within that time would be difficult. Some European officials have previously signaled that they want the U.K. to settle any outstanding payments to the EU before trade talks commence.

Politicians who supported staying urged Mrs. May to keep close ties with the bloc. "It is crucial that in this two-year period the voices and concerns of those who want to preserve close links between Britain and Europe are not shouted down and silenced, and that those with power over this process are held to account," said Anna Soubry, a Conservative lawmaker.

Mrs. May has said one of her priorities is to guarantee EU citizens living in Britain and U.K. citizens living in other parts of Europe continue to have the right to stay even after the U.K. leaves. The EU has said talks on that issue alone will likely take at least several months.

The U.K. and the EU will also have to decide what to do with unspent EU funds that were supposed to go to U.K. farmers, how to implement cross-border security arrangements including access to EU security databases, and whether the U.K. will stay under the jurisdiction of EU regulatory agencies for issues, like nuclear power, that are handled by the bloc's institutions.

On Thursday, Mrs. May is set to publish details of her plans to transfer EU law into U.K. law, so that 19,000 laws and regulations formed over the past four decades will continue to apply to the U.K. after it leaves the bloc, while allowing Parliament to amend the laws as it deems necessary.

Within 48 hours of Britain triggering Article 50, Mr. Tusk is expected to send draft guidelines to the 27 remaining capitals framing the talks from the EU's side. Those guidelines should be finally agreed upon at a Brussels summit on April 29.

After that, EU governments and the European Commission, which is set to lead day-to-day negotiations, will likely take several weeks to set a detailed negotiating mandate for Michel Barnier, the EU's Brexit negotiator. Only then, possibly in late May, are negotiations set to begin in earnest.

"The task before us is momentous but it should not be beyond us," Mrs. May wrote in her letter. "Together, I know we are capable of reaching an agreement about the U.K.'s right and obligation as a departing member state, while establishing a deep and special partnership that contributes toward the prosperity, security and global power of our continent."

Jason Douglas contributed to this article

Write to Jenny Gross at jenny.gross@wsj.com and Laurence Norman at laurence.norman@wsj.com

(END) Dow Jones Newswires

March 29, 2017 10:52 ET (14:52 GMT)

Copyright (c) 2017 Dow Jones & Company, Inc.