After men led Britain into Brexit, women are taking center stage to clean up the mess.

Theresa May, the new leader of Britain, has promised to take Britain out of the European Union. In Scotland, where the leaders of the three biggest parties are women, First Minister Nicola Sturgeon will be one of the most pivotal figures in any Brexit settlement as she threatens a referendum on independence. And Northern Ireland’s assembly is co-headed by a woman.

It’s not an accident, say the women who have pushed to increase the number of women in Parliament — to a record 29.4 percent in last year’s election from just 9 percent in 1992. May will negotiate Britain’s E.U. departure with German Chancellor Angela Merkel, among other European leaders.

“We’re reaping the rewards of years of hard work,” said Anne Jenkin, a member of the House of Lords who, with May, co-founded Women2Win, a Conservative Party group that has campaigned to get more women elected to Parliament.

Yet almost 26 years after Margaret Thatcher quit as prime minister, women make up only 21 percent of Conservative parliament members. For the Labour opposition the figure is 43 percent.

“Women are not dominating the political scene. They’re just gaining the limelight,” said Frances Scott, founder of the 50:50 Parliament Campaign, which is pushing for women to make up half of the House of Commons. “We could be seeing a glass cliff scenario.”

The term “glass cliff” was coined by University of Exeter psychology professors Michelle Ryan and Alexander Haslam to describe the tendency of corporations that are in trouble to appoint women to senior positions. Think Marissa Mayer at Yahoo Inc., Meg Whitman at Hewlett-Packard and Mary Barra at General Motors, all of whom acceded to leadership jobs at difficult times.

“Voters are turned off by some of the old boys’ network, and they want serious leaders,” said Rosie Campbell, a professor at Birkbeck University of London.