Some of his funniest bits are about the competitiveness of the frum, explaining how they try to one-up each other about who has the most backward technology. “My mobile is so kosher it doesn’t even take phone calls,” he says.

Mr. Blaker calls himself “the only strictly Orthodox comedian in the U.K.,” but Orthodox Jewish comedy is growing worldwide, particularly in Israel. A fascinating article in Haaretz on the trend of ultra-Orthodox comedians explains one reason: As the population has grown, it’s become more integrated into Israeli society and a leisure culture has developed. Some argue that it’s precisely the restrictive nature of Orthodox life that makes it ripe for comedians. “When you have 613 laws, this is fertile ground for jokes,” the satirist Kobi Arieli told Haaretz.

Indeed, Mr. Blaker has said in interviews that he didn’t find success until he became strictly Orthodox. The experience of becoming religious, he has said, gave him a subject he wanted to explore onstage. And he exploits the unusual tension of a man from a modest, conservative culture telling jokes. “Strictly Unorthodox” begins with an empty stage and audio from what sounds like a rabbi warning the audience that the following show may not be kosher. This sense of the forbidden can be a helpful foil in comedy, which Mr. Blaker clearly understands, poking fun at his tribe but carefully, never going too far. His amiable act doesn’t question religious dogma with any persistence or engage with doubters. The only time he truly engages is in his promotion.

Before the show’s run, his publicist sent out a news release saying that ads for his show have been rejected by the religious media, one of which, he said refused to even use the word “theater.” His producer Mike Leigh called it “religious correctness gone mad.”

Whatever you think of this spin on the familiar comedian complaint about political correctness, it is savvy public relations. And not just because it gets attention for the show. Mr. Blaker, a clean comic who steers clear of politics, seems more subversive than secular Jewish comics, even those working with much edgier material.

Whether secular audiences used to more overtly button-pushing Jewish satire like that of Larry David will enjoy Mr. Blaker’s gentle observational comedy is unclear. But he’s a skilled joke-teller with none of the borscht belt timing you would expect from a Catskills comic. And since we rarely hear the perspective of the ultra-Orthodox in comedy clubs, there’s a pleasing freshness about an act that offers a look into a world often hidden from public view. His religious fans, some of whom rarely see stand-up or mainstream comedy, may also find him a change of pace. His deft crowd work provides a window into his challenges. When he asks a man in the front row, what’s the first thing he associates with the BBC, Mr. Blaker’s employer, the response was “anti-Semitism.”

Mr. Blaker did not appear surprised by this answer and may have even been seeking it, in order to defuse anxiety among his audience members, some of whom were surely critical of the news media’s treatment of Israel. He nodded, said he avoids the subject of Israel and added that he had never seen any examples of bigotry against Jews as long as he worked at the BBC. This was a difficult crowd for a comic, an audience that started quiet, was even cautious about laughing, but he gradually won them over. He is proof that even the most reverent enjoy a little irreverence.