In Scotland, rancor at the sense that the country’s vote counted for little and subsequent repeated bouts of parliamentary chaos have led to renewed calls for a second independence ballot. Nicola Sturgeon, the first minister, insists Scotland will hold one if Brexit takes place. One of the most adroit politicians in Britain, Ms. Sturgeon knows that despite widespread misgivings about Brexit, the majority needed for independence does not currently exist. But recent polling suggests a Johnson government might tilt the scales in her favor. An independent Scotland may be conjured out of the chicanery of Mr. Johnson’s rule.

In Northern Ireland, Mr. Johnson is beholden to the Democratic Unionist Party, a hard-line Northern Irish Protestant party on which he will depend for a majority in Parliament. That severely curtails his room for maneuver as he attempts, one way or the other, to take Britain out of the European Union. The D.U.P. will not countenance separation from the rest of the United Kingdom — hence why the so-called backstop, effectively an insurance plan to avoid a hard border between Northern Ireland and its southern neighbor, fatally scuttled Theresa May’s thrice-rejected deal. It is hard to see how Mr. Johnson can extricate himself from this problem, whose protraction may have a decisive effect on the country’s internal politics. Calls for a United Ireland, encouraged by demographic change and the waning of unionist sentiment, appear to be gathering more support.

The traditional solution to such an impasse is to call fresh elections. But here too there are problems for Mr. Johnson. Current polls show a fluctuating four-way split with Nigel Farage’s Brexit Party, which peeled off much of the Conservative vote in the recent European elections, the Liberal Democrats and the Labour Party. Tory activists believe only Mr. Johnson can woo back the faithful from Mr. Farage, but if he steers the party farther right it would be likely to lose more liberal-leaning seats. Though the temptation of a resounding victory may pull on Mr. Johnson’s vanity, the risk of a disastrous rout from a split base, handing Downing Street to Jeremy Corbyn and shattering the Tories, will surely be too great. And any successor to Mrs. May will fear the unpredictability of a snap election.

No way out there then . And the overall political situation has only worsened since Mrs. May’s resignation. The European Union — newly configured after parliamentary elections, with an incoming head of the commission who has emphatically ruled out reopening negotiations with Britain — is likely to be short on patience and good will. (It doesn’t help, of course, that its officials regard Mr. Johnson as a dangerous buffoon.)