On a hilltop next to a vast limestone quarry in England’s East Midlands, a crowd of about 60 people gathered last Thursday evening to witness the lighting of a beacon to mark the 80th anniversary of the D-Day landings. Amid the drab parkas and pullovers was a figure in a striking red coat: Natalie Fleet, the Labour Party’s candidate for Parliament, wearing her party’s campaign color.

She turned up late, having hiked up in heels. But she mixed easily, chatting with a 17-year-old high school student, Georgia Haslam, about her desire to get more young women engaged in politics.

“It was reassuring to hear someone like her say, ‘I understand you,’” Ms. Haslam said afterward. “If you’re not from a city, if you’re not wealthy, it’s not clear that these politicians really care about you.”

Ms. Fleet is on track to win back the parliamentary district of Bolsover for Labour, which in 2019 it lost to the Conservatives for the first time in almost 70 years. Her appearance at the D-Day commemoration was a telling contrast to the Conservative prime minister, Rishi Sunak, who skipped out of D-Day ceremonies in France the same day to return to London, drawing a torrent of criticism.

And the Labour Party isn’t even the only headache for the Tories, three weeks before Britain’s general election on July 4. In this hard-bitten region of abandoned coal mines and shuttered steel mills, the insurgent party Reform U.K. is mounting an unexpectedly robust challenge. It could siphon off enough votes from the Conservatives here to leapfrog into second place, after Labour.