At her opening night at the Oak Room last Tuesday, the British jazz singer Claire Martin made a brief comment about how proud she was to be “flying the flag” for European jazz. Many American stars perform in Britain and on the continent, Ms. Martin noted, but it’s almost impossible to think of a British jazz vocalist who’s found acceptance on this side of the Atlantic. One is more likely to find a Dixieland clarinetist from Sweden working in New Orleans than a jazz singer from London appearing in New York.

Outside of Dame Cleo Laine, regarded by many as a great jazz personality, exportable British pop or jazz vocalists have been a motley bunch. Jazz-pop singing flourished in Britain during the dance band era of the 1930s, when Al Bowlly was Bing Crosby’s most gifted rival (not just in Britain, but anywhere) and was flanked by cabaret superstar Leslie Hutchinson and the cockney Satchmo, Nat Gonella.

Then, in the early ’60s, Matt Monro, Anthony Newley, and Shirley Bassey launched the British Invasion well before the Beatles. In between, more traditional types such as Gracie Fields and Dame Vera Lynn flourished locally, if not internationally.

Now, the Wimbledon-born Ms. Martin, who is the only representative of her country, her instrument, her genre, her gender, and her generation to attract international attention, is a likely candidate to raise the torch for European jazz singers. And it’s about time. Despite 13 albums in the last 15 years, she has never made a major appearance in a New York club until now.

As with any contemporary performer who sings jazz or the Great American Songbook, the issue of influence is a key factor. Ms. Martin has said that the first performerswho made her want to sing were Judy Garland and the comparatively conservative offerings of Ella Fitzgerald in the First Lady’s “Songbook” series. Contrastingly, the Oak Room show concluded with “Never Make Your Move Too Soon,” the longtime closing number for the blues-driven jazz singer Ernestine Anderson; it was interesting to see Ms. Martin make a genuine song out of what Ms. Anderson has, through the decades, refashioned into an extended, special-material monologue.

Ms. Martin’s latest album, which was liberally sampled in the Oak Room, is “He Never Mentioned Love” (Linn Records) a tribute to Shirley Horn, who is obviously another major influence. As a salute to Horn, “He Never Mentioned Love” succeeds almost too well. She’s not deliberately trying to imitate the late Horn’s signature snail’s-pace emoting (which she acknowledges in an original tribute tune, the well-titled “Slowly But Shirley”), but it would have been impossible for some of that style not to rub off on her. In slowing down her tempos and absorbing Horn’s deep voice and smoldering style, Ms. Martin winds up sounding, unexpectedly, like something of a British Diana Krall. Overall, the atypical “He Never Mentioned Love” is a fine addition to Ms. Martin’s extensive discography, but it’s hardly the best of her recordings, nor the one I would most recommend as an introduction to her.

Ms. Martin ended the previous decade with two pop-oriented projects: “Take My Heart” and “Perfect Alibi,” both of which anticipated the trend of young female singers, such as Karrin Allyson and Ms. Krall, doing singer-songwriter and country-oriented material in the wake of Norah Jones’s success. Then, between 2002 and 2005, she released three first-rate albums of jazz and standards — “Too Darn Hot,” “Secret Love,” and “When Lights Are Low” — the latter being a set of duets with the highly decorated composer-arranger-pianist Sir Richard Rodney Bennett.

You can’t go wrong with any of these. Each is a copasetic blend of the fresh and the familiar, and freely intermingles Elvis Costello, Burt Bacharach (“God Give Me Strength”), and Joni Mitchell (“Blue Motel Room”) with Irving Berlin and Cole Porter. Ms. Martin can sing a lyric and sing a ballad well: A highlight of the mostly jazzy “Too Darn Hot” is a quasi-hillbilly lament titled “It’s Raining in My Heart.”

Ms. Martin’s greatest strength, though, is the fast and the swinging. For the most part, she does not lessen the virtue of her up-tempos by overindulging in gratuitous, Gospel-derived embellishments or unnecessary scatting. (Interestingly, she’s a little more decorative and scatty in person than on most of her albums, as if someone told her that this was what would go over in New York.) “Too Darn Hot” opens with a high-velocity “Something’s Coming,” that cleverly slows down and revs back up at key points, abruptly stopping here and there in a kind of vocal choreography. “The Gentleman Is a Dope,” on the same album, and “Cheek to Cheek” on “Secret Love,” are taken at the speed of summer lightning, but with every word and every note crystal clear, with a capacity for both rhythm and articulation that shows that if there were a recently deceased vocal icon that Ms. Martin should pay homage to, it’s Anita O’Day.

“Love Is a Bore” on “Secret Love” is sort of both things at once, opening with a slightly out-of-tempo verse, but adroitly setting up the fast-and-frantic chorus on this neglected Cahn and Van Heusen song. On the same album, “Get Happy,” begins exuberantly, although Ms. Martin phrases those words on a descending note, with just drums for half a chorus before guitar, piano, and saxophone take over. In fact, on the current album, “He Never Mentioned Love,” Ms. Martin puts her own distinctive stamp on several Shirley Horn favorites, such as “Everything Must Change” and the sultry blues “All Night Long” by speeding them up with a shot of youthful adrenalin.

By far the jazziest act I’ve ever experienced at the Oak Room (although the absence of drums is a mystery), Ms. Martin realizes well that humor is the flip side of rhythm — perhaps her next album will be a postmodern tribute to George Formby. Her funniest moment is an original, apparently untitled lyric to a bossa nova that details every variety of dissipation known to man, a downfall so complete it would take a combination of every 12-step program extant to deal with it. In all of her modes, Ms. Martin is a world-class performer, offering proof positive that jazz can be sung with a British accent. Cheers.

wfriedwald@nysun.com