By Stephen Fidler

A war of words between London and Brussels escalated this week, a sign that nobody should take a deal over Brexit for granted.

The furor erupted in part over German press reports from a dinner British Prime Minister Theresa May hosted last week for European Commission Jean-Claude Juncker, during which he reportedly concluded she was deluded in her expectations for the Brexit negotiations.

Mrs. May cited press “misrepresentations” in a televised appearance Wednesday outside her Downing Street residence. Together with “threats against Britain” from European politicians and officials and a hardened negotiating stance from the EU’s chief Brexit negotiator Michel Barnier, she said these acts had been timed to affect the result of Britain’s June 8 general election.

The spat likely won’t spoil the chances of an accord. “The baseline scenario is that there will be a deal: Barnier said he wants it and the U.K. desperately needs it. But the underlying risks are substantial,” said Carsten Nickel of the Teneo Intelligence advisory firm in Brussels.

True, there was plenty of election theater in Mrs. May’s response, which seemed designed in part to stir up her party faithful, and Brussels reacted accordingly. “We are not naive and we know that each time that elections happen, people get excited,” said European Commission spokesman Margaritis Schinas on Thursday.

According to Aaron Timms, head of research for Predata, a New York-based firm that analyzes social-media data, “Bashing the EU and accusing the dreaded unaccountables of Brussels of meddling in the U.K. election…is a good, easy way to fire up the Tory true believers.”

But the clash raises important longer-term issues.

First, the leaked accounts of the dinner show that Mrs. May’s plan to keep details of the Brexit negotiations secret is doomed to failure.

Brussels leaks like a sieve. Some leaks are tactical, others inevitable because so many actors are involved: officials and politicians from the commission, the European Council and the European Parliament, not to mention diplomats from 27 other governments.

The commission also drew a lesson from the harsh criticism it received over the secrecy surrounding negotiations over the Transatlantic Trade and Investment Partnership, the moribund U.S.-EU trade agreement, Mr. Nickel said. “When you do these trade deals, you have to be transparent,” he said.

Clearly, if Mrs. May doesn’t communicate about the negotiations, others will. A stance of secrecy would put her and her media managers at risk of playing catch-up for the duration of the talks.

Mrs. May also sought to draw a contrast between the EU capitals and Brussels. “However reasonable the positions of Europe’s other leaders,” she said on Wednesday, “there are some in Brussels who do not want these talks to succeed.”

But it is with Mr. Barnier and the commission, the Brussels-based EU executive, that the day-to-day Brexit negotiations will be held.

On Brexit, the EU has done what it usually does when confronted by new crises: It sets up procedures to handle them. Once the procedures are established, the bloc only very reluctantly departs from them—as Greece found out during its seemingly interminable bailout negotiations.

National capitals will, of course, keep a close eye on Mr. Barnier and his team. But history suggests London shouldn’t hang its negotiating strategy on persuading Berlin, Paris or other governments to make the U.K.’s case. After all, German Chancellor Angela Merkel was the first to say last week that some in London held illusions about what could be achieved in the negotiations.

Furthermore, whipping up anti-Brussels rhetoric may help win votes during an election campaign, but it risks hindering subsequent efforts to find a positive post-Brexit outcome.

For that, compromises on both sides will be necessary. The U.K., for instance, needs some kind of financial settlement with the EU, as much as it hopes that the figure will fall short of the more than €60 billion ($66 billion) in past spending pledges EU officials have said Britain must honor.

Yet Mrs. May’s pro-Brexit constituents aren’t being educated by her hard-line rhetoric to ready themselves for compromise, Mr. Nickel said. As a result, Mrs. May risks further polarizing a nation already divided over Brexit and locking herself into a tough position that will reduce the room for the very negotiating flexibility she hoped to gain with a thumping election victory.

So it is that the risks of no Brexit deal—almost universally agreed to be the worst possible economic outcome—remain substantial.

Donald Tusk, the president of the European Council that comprises the leaders of EU governments, alluded to this fear when he said Thursday that a successful deal would be impossible if the two sides let “emotions get out of hand.”

But he also suggested that leaking one-sided accounts of private meetings wasn’t optimal either. “We must keep in mind that in order to succeed, we need today discretion, moderation, mutual respect and a maximum of good will,” he said.