LONDON — Europe and Britain, in a very public way, staked out their newest, most definitive Brexit negotiations Wednesday over their future relationship, with the new president of the European Commission warning British Prime Minister Boris Johnson that it would probably be "impossible" for the two sides to complete a comprehensive divorce deal by his "very tight" deadline at the end of 2020.

The coming talks will shape the future for all sides after Britain exits the European Union at the end of January. The break follows four decades of the closest cooperation on trade, security and immigration, which allowed Europeans and Britons to live and work freely in any country in the 28-member bloc.

Speaking before her first face-to-face meeting with the prime minister at No. 10 Downing Street in London on Wednesday, European Commission President Ursula von der Leyen said that if Johnson’s new government wanted the most favorable terms for divorce, with deep access to the largest, richest single market on the planet, then Britain should seek to align itself with E.U. rules and regulations.

Johnson has given multiple contradictory answers regarding the question of alignment. During his campaign, which led to a landslide victory for his Conservative Party last month, he never was clear about what kind of Brexit he will seek, except to speak in the most general terms about the future being great.

Von der Leyen, a former German defense minister, lamented that the U.K.-E.U. marriage is over. She fondly remembered her year at the London School of Economics, where she gave her speech, and recalled, too, her pleasure in exploring a multicultural London, with frequent trips to Camden Town record stores and Soho pubs.

But she cautioned Johnson and his libertarian allies that without the free movement of European citizens into Britain, one of the foundational pillars of the European Union, “you can’t have the free movement of goods, services and capital.”

Britain sells a lot of lamb, cheese and cars to Europe — but its No. 1 export is financial services, including banking, insurance and the movement of money.

Von der Leyen said she hopes the two sides will be able to reach a trade deal with “zero tariffs, zero dumping, zero quotas.”

But she warned that if Britain diverged from E.U. alignment and created an uneven “playing field” on things such as workers’ rights, the environment and government subsidies for industries, then Britain will not have full access to Europe’s single market of 500 million consumers. And she said that the less time they have to negotiate, the smaller the eventual deal.

“The more divergence there is, the more distant the partnership has to be,” she said. “Without an extension of the transition period beyond 2020, you cannot expect to agree on every single aspect of our new partnership.”

Johnson told von der Leyen that he is firm on spinning away from the European Union altogether at the end of the year. After it formally leaves the bloc at the end of this month, Britain plans to leave most E.U. regulations in place as negotiations start up — but only until December.

Johnson “reiterated that we wanted a broad free trade agreement covering goods and services, and cooperation in other areas,” his office said in a statement.

Johnson once denounced a border in the Irish Sea for future E.U.-U.K. customs checks, which his predecessor swore “no prime minister would ever agree to,” as it threatened the integrity of the United Kingdom. Then he caved and agreed to it.

But there were clear differences on display during the visit, posturing aside. When Johnson welcomed von der Leyen to Downing Street, he noted breezily that “Ursula and I were at school together” as children in Brussels, where both of their fathers worked for European institutions.

“But not at the same time,” von der Leyen immediately replied, adhering to the facts, in what may be a preview of the unsentimental negotiation approach from the E.U. side. (They missed each other by a few years, it seems, although Johnson wasn’t able to remember exactly which years he was there.) They did share a teacher.

At von der Leyen’s speech in London, she welcomed Michel Barnier, the E.U.’s chief Brexit negotiator, to the stage, where he warned that Britain faces in the coming months not only a renegotiation with Europe but the fact that it will need to redo 600 international agreements that the European Union had concluded on behalf of all its members.

Britain, Barnier said, has to rebuild “each and every trade deal around the world.” None can be implemented until Britain leaves the European Union, he said.

Birnbaum reported from Brussels. Quentin Ariès in Brussels contributed to this report.