‘I’m not a very good storyteller,” shrugs Joan Jett, sporting black leather and trademark poker face. If you’ve come expecting something as sappy as sentimental anecdotes at this anniversary tour celebrating 45 years of her career-defining albums Bad Reputation and I Love Rock’n’Roll, you’d better jog on.

The Rock and Roll Hall of Famer isn’t here to chat, or pat herself on the back. This first UK headline show in 16 years delivers straight-shooting hard rock, from early cuts with the Runaways to her most recent releases with the Blackhearts. At 67, Jett’s voice is still deep and commanding – if time has added more gravel, it’s only for the better – and the Blackhearts’ current iteration as a simplified three-piece play hard and fast. It’s all real rock history, but it comes across more like history than it should: even the adrenalised teenage terror of Cherry Bomb is delivered with cool, even stiff, nonchalance.

‘I want to sweat!’ … Joan Jett. Photograph: Katherine Anne Rose/The Guardian

Maybe Jett feels the same way. She asks for less AC on stage – “I want to sweat!” – and the night does heat up. She’s a great cover artist, and her version of the Replacements’ still-resonant Androgynous is heartfelt and surprisingly rootsy. Loosened, she cracks a rare grin during Sly and the Family Stone’s Everyday People, before digging into a sour, serrated guitar solo. On a technicality, I Love Rock’n’Roll and Crimson and Clover are covers too, but they feel like they’ve always been hers. The latter’s switch-up between dreamy, grungy vulnerability and thrashing noise is a real highlight, as is the swaggering, pissed-off arena rock of I Hate Myself for Loving You.

With such an arsenal, it’s miserable that Jett still performs convicted paedophile Gary Glitter’s creepiest hit Do You Wanna Touch Me. She has far better songs that don’t require the limp disclaimer she recently gave: “Am I going to drop it … after I’ve had my own career with the song? No.” The show closes on Bad Reputation – a reminder, as if anyone still needs it, that Jett marches to her own drum. Tonight is all the hits but one too many, not that she’ll give a damn.