‘I used to be polarising, perhaps,” Sinéad O’Connor said on Good Morning Britain in September. “But I’ve got a bit older and I don’t think I’m polarising [now].”

That’s a matter of perspective. Her conversion to Islam last year, changing her name to Shuhada Sadaqat in the process (though her original name still appears on her social media), produced a torrent of reaction, not all of it positive. In a tweet at the time, she declared: “I never wanna spend time with white people again (if that’s what non-muslims are called). Not for one moment, for any reason. They are disgusting.”

Performance is a serious business … Sinead O’Connor. Photograph: Gus Stewart/Redferns

Apologising later, she said she had been “angry and unwell” – but no matter how many bridges she burns during periods of illness, she still has an extraordinary rapport with her fans, who cheer lustily as her backing band arrive, and then O’Connor herself, in hijab and full-length dress. A woman in a headscarf fronting a folky rock group shouldn’t feel transgressive, yet it does – 30 years into her career, she still follows her own truths, wherever they lead. When she caustically delivers the lines: “You have no right to want anything from me / Why don’t you take it out on somebody else?” from tonight’s opener, the John Grant song Queen of Denmark, the cheers rise several notches. O’Connor whispers her thanks.

Her first UK performance since 2015 has a dual purpose: to reassure herself that people still want to see her – she had worried that nobody would come – and to gear up for a busy 2020. A new album is imminent and will be accompanied by a lengthy tour. A feathery track from it features as tonight’s last song. The stage has always seemed a refuge for her: a place where she’s free to offload about love, faith and betrayal by people in power.

And when she’s on form, as tonight, she’s radiant. The more broken the song, the more strength she siphons from it; the heavy-hearted Reason with Me uses a junkie analogy to portray her obsession with a man, and she gains more power with each verse, finishing with a wild cry. I Am Stretched on Your Grave, sung a cappella under purple spotlights, is almost too mournful to stand, but as it slowly unfurls, O’Connor’s voice grows steelier until she’s fairly blasting the words. She vowed several years ago never to sing Nothing Compares 2 U again because she no longer “emotionally identified” with her biggest hit, but here it is, still stupendous.

There are lighter moments, such as the dance-cum-twirl she busts out during the skiffle-shuffle 4th and Vine, and her brisk introduction to Black Boys on Mopeds: “I think you might like this.” She’s right: the first line, “Margaret Thatcher on TV”, induces jeers from a reminiscing 90% of the audience who are over 40. Mainly, though, performance is a serious business for this outstanding singer. She speaks infrequently – perhaps because she gives so much of herself in her lyrics – and focuses on finding solace in the music.