LONDON — She danced, Britain cringed, and then she danced again.

The British prime minister, Theresa May, the vicar’s daughter known for her devotion to duty and wooden campaign style, busted out first in South Africa and then yesterday in Kenya. Her Dance Moves, such as they were, did serve the purpose of drawing attention to an otherwise forgettable trip to drum up trade deals.

In Cape Town she visited a school where she was welcomed by a crowd of students, singing and dancing. Tall and thin, clad in a red jacket, she took a couple of stiff steps in what looked like a version of robotic disco.

Internet wags suggested she was “doing the Maybot,” after the cruel nickname she earned for her prerecorded answers to the myriad questions about Britain’s planned withdrawal from the European Union, or Brexit. Inevitably, others got more creative, making a dubstep remix, or a cat version, tweeted by an account claiming to represent Mrs. May’s very own Cabinet Office cat.

Her defenders say that however much she is ridiculed, her awkwardness could be softening her image in the eyes of a British public that values self-deprecation.

“This, obviously, would be all of us in her situation, but it strikes me just how unusual it is for top politicians to be in touch with the general public in this way,” wrote Martha Gill, a political journalist, this week, a sentiment echoed by commentators on Twitter.

The prime minister may have had something like that in mind when she took to the Dance Floor with Scouts in Kenya. Or maybe she recognized dancing as the best way to call attention to an initiative to combat single-use plastic pollution, a popular cause at home amid the doom and gloom of Brexit.

Some of her colleagues and predecessors were more accomplished dancers, and better at the people thing. Even the Iron Lady, Margaret Thatcher, managed a graceful turn on the dance floor with Ronald Reagan during a ball in the White House.

Ed Balls, a Labour politician, made headlines when he appeared as a contestant on a television dance show, “Strictly Come Dancing.” He lacked polish, but the public praised him as a keen learner.

Two years before becoming prime minister, when she was home secretary, Mrs. May gave a preview of her dance moves on the BBC’s “Desert Island Discs,” a popular radio program that has invited public figures, since 1942, to share eight recordings that they would take as castaways to a desert island.

“I thought when I was preparing this sort of list that I’d actually quite like something to perhaps jig up and down to or dance to a bit on this desert island,” she said.

“And my husband Philip and I are sort of the Abba generation, so it is a piece of Abba and I’ve chosen ‘Dancing Queen.’ ”