Simon Price on Dexys: Cheer up, Kevin! I'm about to give you a big smacker on the lips

Some things are a gift. Like the sign above the Duke of York's – where Dexys are playing an unprecedented nine nights – for Peter Nichols's black comedy Passion Play. Dexys are an act, after all, who called their 1981 tour The Projected Passion Revue, and the two elements that implies – heightened emotion and calculated theatricality – are still key to a Dexys live show.

Since Kevin Rowland's band made their astounding return last year, looking like regulars at Rick's Café Américain and sounding like the greatest soul troupe on earth, audiences have been treated to comeback album One Day I'm Going to Soar performed, start to finish, in a manner befitting its narrative of a man struggling with the idea of love and commitment.

This time around, though, everything is turned up another two notches, as if the West End setting demands something even more dramatic. For example, during the cocktail party interlude, Kevin plays out a fistfight with trusty trombonist Jim Paterson. And actress-singer Madeleine Hyland begins "She Got a Wiggle" reclined on a chaise longue with a cigarette holder and, after his tenacious courtship, gives Rowland a proper smacker on the mouth so he spends the rest of the show wearing her lippy.

Co-vocalist Pete Williams is his Sergeant Wilson: a voice of moderation, lending an ear and trying to calm him. It's a tall order. During the medley of "Until I Believe in My Soul" and "Tell Me When My Light Turns Green", Williams, dressed as a policeman and called to deal with Rowland's confession of "burning", asks what seems to be the problem. The singer snaps "Have you got a f***ing hearing problem, officer?"

It's all smiles by the end of "This Is What She's Like", with the duo walk-dancing across the footlights like Flanagan & Allen. "Passion Play" doesn't begin to describe it. For another week, at least, it's the greatest show in theatreland.

If there's one thing I hate more than writing about British Sea Power (Shepherd's Bush Empire, London *****), it's not writing about British Sea Power. It's my unshakeable belief that BSP are one of the finest bands this country has produced in the 21st century (perhaps the finest). Ask me to give reasons, however, and I struggle. In my job, that's a problem.

British Sea Power's appeal eludes the conventional clichés of rock criticism. The sell, to recap: an enigmatic indie rock band from the Lake District, led by brothers called Yan and Hamilton whose principal obsessions are ornithology, English history, Slavic literature and climate change, whose catalogue includes a hymn to the heroism of goose migration, and who are as likely to name-check Vaughan Williams as invoke Seventies wrestler Big Daddy's "eas-eh, eas-eh" chant, who have a fondness for collaborating with Bulgarian choirs and performing on a stage bedecked with foliage and antlers. See, I told you it wasn't eas-eh.

But they are, trust me, wonderful, and while they may never have had a big breakthrough moment, they've earned a fervent fanbase. Tonight they're in danger of peaking early. They begin with barricade-storming debut single "Remember Me", lurch straight into early Pixies pastiche "Apologies to Insect Life", and follow that with "K Hole", the most demented moment from new album Machineries of Joy, by which point their mascot, a giant bear called Ursus Major, is romping about the stage.

Fortunately they've kept plenty in reserve. "Waving Flags", their pro-immigration anthem and two-finger salute to Ukip, is as rousing as "Telstar". And by the time we get to the absurdly epic "Carrion", another ursine dancer is onstage: a large white one called Bipolar Bear. It's a peculiarly uplifting sight, which leaves me wondering why all gigs don't end with a giant polar bear leading the dance, while knowing that only British Sea Power would even think of it.

Critic's Choice

The musical wing of this year's Sundance London festival at the 02 includes an Eagle Q&A (Thu), Peaches (Fri), a Celebration of Muscle Shoals featuring Greg Allman (Sat), and British Sea Power, above, and Public Service Broadcasting (Sun 28). Meanwhile, the ever-mighty Public Enemy bring the noise at the ABC, Glasgow (Mon); Rock City, Nottingham (Tue) and UEA, Norwich (Wed).