Caroline Polachek poses enigmatically against a backdrop projection of a wrought-iron gate that recalls some piece of misplaced Maleficent scenery. “This is the last show we might be at for a long time, so let’s make it a good one,” she grins, a couple of tracks into her set.

Polachek’s show at London’s most famous railway arch – the club Heaven – reveals itself to be both a good one and a slight disappointment. This has little to do with Polachek’s own bravura performance – slick, clever, committed – and everything to do with some giddily raised expectations of the US pop auteur. Although she was previously in a band, Chairlift, whose song, Bruises, was ubiquitous in 2008 thanks to an iPod Nano ad, Polachek never became a household name.

But a few years on from Chairlift’s 2016 demise, and a couple of projects into a solo career, Polachek now forms part of a recherché club of international art pop operatives who dance on the edge of mainstream fame. It’s not about the really big names – although the stars do line up to praise Polachek.

Lady Gaga put the Manhattan-born singer’s So Hot You’re Hurting My Feelings on her recent International Women’s Day playlist. (Taylor Swift included the song Door.) Polachek’s song The Gate is on Grimes’s “fetal sync” pregnancy playlist too.

More pertinently, Polachek’s solo album Pang exists in a delicious tension with Charli XCX’s Charli, also released in 2019. Both singers are also writers; females who are conventionally strong pop vocalists, but want to do borderline avant garde things inside a notionally undemanding genre. And the personnel on both albums all know each other. You get the feeling that a plan is still unfolding.

Charli was produced by AG Cook, previously of maverick London pop disrupters PC Music. Pang was produced by PCM alumnus Danny L Harle; a house in Los Angeles used by both camps figured in the writing of the album. So Charli XCX’s verdict on Pang came as little surprise, but was not far off the mark: “top to tail perfection”, she called it.

Even more germane, in the last fortnight, Polachek has been involved in other international grown-up pop happenings – as the featured guest on Christine and the Queens’ excellent recent EP, La Vita Nuova. In the short film that accompanied the CATQ release, Polachek becomes a victim to the red-eyed Héloïse Letissier’s vampiric desires.

Days before tonight’s gig, Polachek joined Christine and the Queens on stage for a duet in a tiny east London club to mark the release. Not long before that, Polachek played her own deconstructed solo gig in a church for Radio 1 DJ Annie Mac’s AMP festival. Those stripped-back versions of Pang’s songs – on Chinese hammered dulcimer, electric upright bass and digital mellotron – were notable precisely because Pang was one of last year’s most hyper-produced pop offerings.

So if Polachek remains a little niche, that feeling is changing, and not before time. Tunes like So Hot You’re Hurting My Feelings are hugely influenced by the big vamps of 80s AOR as much as they are by digital mischief. When it comes tonight, the song sounds like an era-mulching banger artificially rendered bonsai by being played in a too-small venue. Less excitingly, Polachek covers the Corrs’ Breathless tonight, which is perhaps an art prank too far.

All this notwithstanding, tonight’s gig proceeds by the book – and given all that has recently preceded it, that constitutes just the merest of let-downs. Letissier does not make a return special guest appearance. No one goes nuts on a hammered Chinese dulcimer. Nothing is stripped back in any conventional sense – apart from one song, Look at Me Now, which finds Polachek playing guitar alongside her sole bandmate, the multi-instrumentalist Blu DeTiger on bass, largely unaided by electronics. The crowd yell out one of the most personal lines – “girl, you’re getting skinny” – a concern in the song voiced by Polachek’s friends, as the singer processed the end of her two-year marriage and began anew. (Polachek sometimes models, but Pang serves as reassurance that even very beautiful people can be very articulate about being very sad.)

The sole bit of lily-gilding tonight is a guest appearance by Harle, who joins Polachek in the encore to big cheers. On Parachute, a song about taking risks, he triggers the song’s digital atmospherics. Shortly afterwards, he ruins her concentration by triggering a loud hip-hop producer tag of “Caroline Polachek!”. One new pop song called Smoke – “we wrote this yesterday” – points enticingly forwards, as Polachek, Harle and the bassist on backing vocals trade beats with “na, na, nas”.

The rest of the night remains all about Pang’s suite of sad, arty alt-bangers in all their original synthetic glory: reverberating bass, snickety hi-hats, mostly ersatz, all delicious. She plays nothing from her Chairlift days, or from her other previous projects, Ramona Lisa and CEP. But the DJ’s pre-gig playlist of wall-to-wall Cocteau Twins points up the sophisticated nature of what is actually going on in Polachek’s music, which still bears examination.

Even though her vocals on the album sound treated, Polachek is blessed with an innately processed-sounding vocal ability. Tonight, she trills, swoons and delivers both Arabic intonations and Liz Fraser-like melismas on songs like Insomnia with little, if any, digital assistance, slaying the high notes, faintly recalling that other great wind generator of contemporary pop, Florence and the Machine, on Ocean of Tears.

Not only that, but the songs sound as strong as you remember them. Even The Gate, which seemed initially as an introductory passage, sounds profound tonight. “We will be okay/ cause finally there’s a way to be both free and safe,” Polachek exhales.