LONDON — When Theresa May became the prime minister of Britain in July, she appeared to be confirming a trend rather than establishing one. Northern Ireland is led by a woman. Scotland’s first minister is a woman, and so are the main two Scottish opposition leaders. Even the populist U.K. Independence Party recently elected its first female leader, though her tenure was short.

A quarter-century after Margaret Thatcher left power as Britain’s first female leader, it is the center-left Labour Party that has become the exception, with its recent leadership battle between two men.

The rise of women in British politics is certainly striking — the Green Party is also led by a woman (who shares the job with a man), as is the Welsh nationalist party — but does it amount to progress?

Amid the turmoil following the vote to leave the European Union, there is a sense in some quarters that rather than shattering a glass ceiling, female leaders risk tumbling down a “glass cliff” — a theory that holds that women are often placed in positions of power when the situation is dire, men are uninterested and the likelihood of success is low.