We’ll get on to the brilliance of Regina Spektor in a moment. But first a question: why are pop music fans treated so abysmally? The afternoon of Spektor’s second sold-out show at the Royal Festival Hall, the venue tweeted that she would be on stage at 7.30 p.m. She actually took to the stage a few minutes past 8 o’clock.

If that were a one-off, so be it. But anyone who goes to a lot of shows is familiar with how malleable the concept of stage-time is in pop music. Lana Del Rey had her Glastonbury set cut short because she was so late coming on – apparently she was having her hair done. It’s maddening. Why can they not meet their call times? No one going to see The Motive and the Cue is kept waiting because Mark Gatiss is playing Candy Crush in his dressing room. You don’t go to see an orchestra and sit happily past the appointed start time because the first violin is FaceTiming their mum. Even football, an industry that has long treated those who pay to watch it with complete contempt, starts its matches on time and, if they kick off late, lets you know why. But pop concerts? Hey, sheep, you can just sit and bloody wait, because you don’t matter.

So it was a good job Spektor was absolutely magnificent once she did come on. It was just her on piano or keyboard, and – for a scant few songs – a guitarist, but she filled the room with charisma, charm and wit. I didn’t begrudge a second of the two hours she was on stage, just the 33 minutes she should have been but wasn’t.

Spektor emerged out of New York’s anti-folk scene at the turn of the century, but all she really shared with the Moldy Peaches or Jeffrey Lewis was a fondness for whimsy. Her musicality is questing and varied, never sitting still or settling. ‘Baby Jesus’ was hugely reminiscent of Tom Lehrer, musically at least; ‘Silly Eye-Color Generalizations’ was the kind of thing that might once have been the musical interlude on a BBC2 comedy sketch show. But then there were songs as straightforwardly emotional as ‘Fidelity’ or ‘Samson’. Her voice could be an intimate whisper, or a commanding mezzo soprano, and its tone communicated her intent as much as her words.

Her family emigrated to New York from the Soviet Union when she was a child, and she’s the rare artist in whom you can hear both Europe and America: her musical ancestry comes as much from previous generations of Jewish emigration from eastern Europe to the States – Irving Berlin, the Gershwins – as it does from the Lower East Side of rock clubs and dive bars. None of the disparate threads felt soldered together, though: no matter how different the songs, they all seemed to reflect a giddiness, a delight in the infinite possibility of song. You might know her best as the singer of the theme tune to Orange Is the New Black – ‘You’ve Got Time’ – but that only hints at the vast expanse of her talent.

The Windmill Brixton, a tiny room in south London, has a huge reputation as an incubator of new talent, and one example of that was on show there last week. Borough Council were the middle band of a three-group bill, and they sparkled. They’ve only released one song so far, a single called ‘Prescribed’, which pairs characteristically blank and affectless indie vocals (‘Give me something else to feel’, the only lyric I could make out, seemed apt) with the propulsive thrust of the four-to-the-floor rhythm music writers are legally obligated to call ‘motorik’.

‘Prescribed’ was hardly atypical of their short set, but nor did it outshine the rest of it. Borough Council are a trio, and the way guitar, bass and drums locked together into a single unit was intense and desperately exciting. It’s just one trick, but it’s a very good trick to have, and the way the guitar wove webs around the throb of the rhythm section suggested they have the imagination to go further. One word of warning: they are almost ungoogleable – try ‘Borough Council band’ and you just get lots of stuff about council tax. Maybe that’s deliberate: they’re a deliciously austere band in an age of oversharing. I loved them.