When the government appealed recently for 250,000 people to help the National Health Service, more than 750,000 signed up. It was forced to temporarily stop taking applicants so it could process the flood. In addition to the national program, hundreds of community-based aid groups have sprung up around the country, enrolling tens of thousands of volunteers, like Ms. Sellars.

All told, it is a stirring display of British national solidarity — a good-news story amid a grim tide of bulletins about overwhelmed hospitals, inadequate testing, a rising death toll, and a depleted political establishment, with Prime Minister Boris Johnson in intensive care and several of his aides still struggling after contracting the virus.

[Analysis: Coronavirus puts to the fore an improbable U.K. leader: Dominic Raab.]

It is also a welcome balm, coming after three and a half years of bitter divisions over Brexit, a debate that cleaved the country socially, culturally and generationally. Coronavirus, many commentators have noted, is an equal-opportunity scourge: It strikes both “Leavers” and “Remainers.”

“During the Brexit debate, people used to say what we really need is a common enemy — and now we’ve got it,” said David Goodhart, a writer whose last book, “The Road to Somewhere,” explored the divide in British society between the rooted and the rootless. “Except this is an invisible enemy.”