In July the government of Prime Minister Boris Johnson responded by impaneling the Commission on Race and Ethnic Disparities. “We decided to step away from the heat and all that vitriol,” says its chairman, Tony Sewell, “and just take a cold look at the data on racism.” In doing so, “we examined ideas that weren’t to be questioned,” namely “the race industry’s articles of faith.” In its March 31 report, the commission concluded that while Britain isn’t yet “a post-racial society,” neither is it any longer a place where “the system” is “deliberately rigged against ethnic minorities.”

As a result, Mr. Sewell, who is black—only one of the 10 other commissioners is white—has come under blistering attack. It ranges from the achingly predictable (a profusion of “Uncle Tom” accusations on Twitter ) to the grotesque. A Cambridge professor of postcolonial studies likened Mr. Sewell to Nazi propagandist Joseph Goebbels. A Labour member of Parliament suggested that he belonged in the Ku Klux Klan. Add in put-downs like “house Negro,” “token” and “race traitor,” and you have a picture of the liberal rage ignited by the commission’s refusal to endorse the belief that Britain is irremediably racist.

Mr. Sewell, 62, runs a charity that coaches black schoolchildren in science and math. “It’s a STEM pipeline program,” he says via Zoom from the study of his house in London. “It starts when they’re young and takes them up to university, using summer schools.” Thousands of black kids have been given a college opportunity they “didn’t have in the first place.” Yet he’s called an “Uncle Tom.”

He characterizes the abuse as “a sort of antiracism that borders on racism.” He also detects some desperation, “not only in black lobby groups but on the white left”: “they’re frightened of the report.” Since few ordinary citizens will read its 258 pages, its opponents have busied themselves spreading “distortions” in a bid to capture public opinion. He singles out the leftist Guardian newspaper, which published a sweeping condemnation by David Olusoga, a historian of slavery, who scorns the report as “poisonously patronising” and “historically illiterate.”

Born in London’s Brixton district, where his Jamaican parents settled after immigrating in 1957, Mr. Sewell says the country was harsh and racist, “harder than anything they had ever experienced.” He felt the sting of racism in his youth. But Britain has “come a very long way in the last 50 years.”

The report echoes that point, observing that “there is a salience and attention to race equality in the U.K. in policy-making, and in the media, which is seldom found in other European countries” and asserting that the success of much of Britain’s nonwhite population “should be regarded as a model for other White-majority countries.”

Mr. Sewell says his team was careful to take a “fact-based approach” to their examination of Britain’s racial questions. In an obvious reference to activists and lobbies of the left, the report bemoans the “reluctance” in Britain to acknowledge that the country has “become open and fairer,” and singles out for attention “an increasingly strident form of anti-racism thinking that seeks to explain all minority disadvantage through the prism of White discrimination.”

The report also questions the value of some cherished racial shibboleths: Do repeated assertions that the “dominant feature” of British society is institutional racism and white privilege “achieve anything beyond alienating the decent centre ground”? If every problem in society is attributed to racism, Mr. Sewell asks, “how can Britain ever be a country at peace with itself?”

The report acknowledges disparities between races in Britain. But whites aren’t uniformly at an advantage, and Mr. Sewell and his commissioners part company with the race lobby, which blames racism for all differences between ethnic groups in education, health, prosperity and crime. Instead, the report argues that many of these disparities arise from differences in economic class, geography, family patterns and culture.

Black Caribbean children perform worse in British schools than those of any other group. “For years,” Mr. Sewell says, “it has been said that this is explained in terms of teachers’ racism.” Yet black African students—“same age, same demographic, same classroom”—had academic achievement rates higher than those of whites. In fact, he says, all ethnic groups other than Caribbean blacks perform better than white British students, with the exception of Pakistanis, who are on par with whites.

Mr. Sewell says that you can’t understand ethnic differences in outcome—particularly in education and crime—without focusing on what he calls “family strain,” the effect of single-parent families. “This is the first time we’ve ever had a race report,” he says, “that looks at the family and links disparities to the family.” Race activists, he explains, “just take all questions about single-parent families off the table.”

It’s a distant echo of the U.S. in 1965, when Assistant Labor Secretary Daniel Patrick Moynihan prompted controversy with his seminal report, “The Negro Family: The Case for National Action.” But Mr. Sewell emphasizes the differences between the American and British experiences with race. “I think it’s dangerous to compare the two places,” he says. “I do think there are very specific issues in the U.S. that come out of having a society that was based on slavery inside that country. Britain isn’t built like that, and blacks here haven’t got that same length of time that black Americans have been in their own country.” He also says that the U.S. has a “significant black middle class that Britain doesn’t really have.”

Although it deals with family structure in less detail than the Moynihan report, the Sewell report contains sobering numbers. While 14.7% of all British families are single-parent units, the share is 63% in the black Caribbean community. Britons of Indian origin have the lowest single-parent incidence—only 6%. Mr. Sewell says these numbers are like tinder in public debates on race. If he were to go on TV and observe that 6 of 10 black Caribbean children grow up with only one parent, he would “be shot down for stigmatizing the single parent and blaming the victim. The headlines would say, ‘Commissioner Blames Single Parents.’ Actually, no—they would say, ‘Commissioner Attacks Single Parents.’ ”

Mr. Sewell stresses that he has “no problems, in and of itself, with the single-parent design,” but single parents “are not getting the support they need” and that the commission recommends they receive. Absent any acknowledgment of the sociocultural strain such families face, there is no policy to provide them with “therapeutic assistance, conflict management and educational support.” When their children underperform at school and are later incarcerated, racism is the catchall explanation.

A notable recommendation of the Sewell report is that Britain abandon the ugly acronym BAME, which stands for “black, Asian and minority ethnic.” Numbers from the most recent U.K. census, conducted in 2011, indicate that 7.5% of the population is Asian (0.7% Chinese, most of the rest from the Indian subcontinent), 3.3% black (of whom one-third are of Caribbean origin), and 86% white. “We need to disaggregate the term ‘BAME.’ ” Mr. Sewell says. This ethnic portmanteau “just lumps everyone together.” He offers examples: “The category ‘Asian’ includes prosperous Gujarati consultants in London and impoverished Pakistani taxi drivers in Bradford.” Within the “black” cohort, the Caribbean school-expulsion rate is 3.5 times that of Africans. “The idea that all ethnic minority people suffer a common disadvantage is an anachronism,” Mr. Sewell says. Forty percent of Britain’s medical clinicians are Indian: “This last fact isn’t celebrated, by the way. This is hidden.”

Perhaps the report’s most striking aspect is its emphasis on class and geography as more powerful drivers than race of disadvantage in Britain. “Of course, once you start shifting the template,” he says, “you get accused of race denial. And then you become an ‘apologist’ for racism in the eyes of the critics.” Yet with a focus on class, says Mr. Sewell, “we’re able to bring everybody together, including the white poor—what we might call the British deplorables, to use Hillary Clinton’s remark.”

A race-centered narrative lumps white people together. This is a problem, he says, “especially when you talk about white privilege, and you have white people in Britain who are doing worse than everyone else in health, education and employment. . . . You can’t ignore disadvantaged whites, even if the race lobby thinks you’re watering down their issue.”

Mr. Sewell isn’t surprised by the venom that’s been directed against him. A network of charities, consultants, researchers, academic departments and political activists are “literally invested” in keeping the idea of racism alive. “People have a financial stake in this area, so there’s a sense that they’ve got to protect their own base.”

Yet Mr. Sewell acknowledges that racism can’t be wholly eliminated. “I’m not that naive,” he says. “But what I do think you can do is to build a society where those people who experience it are protected.” Fairness is the key—for blacks, whites and everybody else. He worries that Britain’s “young people are growing cynical” by internalizing the lobby groups’ insistence that “the door is closed” on the basis of race.

“Our message is that the door is open”—that Britain is, or at least aspires to be, a society “where, genuinely, everybody gets a chance, where everybody gets a fair opportunity.”

Mr. Varadarajan, a Journal contributor, is a fellow at the American Enterprise Institute and at New York University Law School’s Classical Liberal Institute.