Even in Wales, which voted to leave Europe in 2016, there is evidence of a budding independence movement. While polls rarely show support for it rising above 25 percent, the chaotic politics of Brexit in London have raised doubts among some Welsh.

The situation in Northern Ireland is more complicated. There is less of a push to break away, though a recent poll by Michael Ashcroft, a British pollster and former Conservative Party official, showed that a bare majority of people there would vote to leave the United Kingdom, if given a choice.

That is partly a function of demographics: Catholics, who tend to be nationalist, are growing more rapidly as a percentage of the population than Protestants, who tend to be unionist. But it also reflects tensions over Brexit, particularly since the arrival of Mr. Johnson and his threat to leave the European Union, even without a deal, by the end of October.

Sinn Fein, the Irish nationalist party that once served as the political wing of the Irish Republican Army, said that if Mr. Johnson carried out that threat, Northern Ireland should hold a referendum.

“People from across this society, even those of a British identity, are now seriously questioning whether there are any merits of staying within the Union after Brexit,” Michelle O’Neill, the deputy leader of Sinn Fein, said during a debate at the Labour Party conference in Brighton, England last month.

In that regard, Mr. Johnson’s deal is a mixed blessing. Northern Ireland would remain legally part of the United Kingdom’s customs territory, but it would stay closely aligned with the maze of European rules and regulations.