They’ve broken up twice, haven’t released a studio disc in 10 years, last played here in 1993, and are in their fifties, a full generation removed from their creative and commercial peak as UK New Wave icons. So why is this a can’t-miss show (for those of a certain age, anyway)? Because—aside from being the band’s lone constants in the 34 tumultuous years since they barreled out of a south London pub-rock scene that also produced Dire Straits—guitarists/vocalists Glenn Tilbrook and Chris Difford write brilliant, timeless pop songs, peaking in the late ’70s and early ’80s with a run of three-minute masterpieces. You can dance (or at least sway) to everything, and no matter the lineup (bassist John Bentley, who left the band in ’85, is back), they’ve always delivered the goods live. Tilbrook is a warm, generous performer whose sweet voice belies his grit, as anyone who saw him solo six years ago at the Croc—where he gutted it out on a badly sprained ankle, then grabbed his crutches mid-show and led a delirious crowd down the block to the Lava Lounge for a raucous “Pulling Mussels (From The Shell)”—will attest. Tue., Sept. 16, 7 p.m., 2008