Radiohead have been at the top of the musical tree for so long now that it’s easy to forget what an irreducibly strange band they are. Last Thursday, during the first of their three hugely anticipated gigs at the Roundhouse, they uncharacteristically played three popular favourites on the run — in their defence, it was the encore — causing someone in the audience to call out for another one. ‘No,’ replied Thom Yorke with a smile, ‘this is all getting too much fun.’ And with that, he launched into the melancholy bossa nova shuffle of ‘Present Tense’ from the new album A Moon Shaped Pool — as if to make it clear that giving people what they want (or misguidedly think they do) would be a betrayal of everything that Radiohead stand for.

The really strange bit, though, isn’t that he’s right, but that the audience wouldn’t have it any other way. ‘Present Tense’ was greeted not with a groan of disappointment, but with an all’s-right-with-the-world murmur of appreciation. In other words, it seems, the unspoken deal with Radiohead is for us to want them not to give us what we want (or misguidedly think we do).

This deal made its presence felt immediately, when the band began with the first five tracks from A Moon Shaped Pool, which combines ambient electronica, sweeping string arrangements and splashes of rock to undeniably beautiful effect — even if it doesn’t always avoid the thin line between impressive coherence and a certain samey-ness. Luckily, the band were in fine form: the non-Yorke members duly eschewing all rock-star heroics in favour of unfussy virtuosity; Yorke himself giving every impression of being lost in the music as he combined that celebrated otherworldly falsetto with some serious Stevie Wonder headshaking and bursts of his famous jerky dancing.

Even so, at this stage I was beginning to think that the rest of the audience might be sharing my guilty secret — that, while we’re genuinely awestruck by Radiohead’s constant ability to lead us in curious new directions, if we really want our hearts to soar, we play their records from the 1990s. It was a theory that received a definite boost when the Nineties B-side ‘Talk Show Host’ received much the loudest cheer of the night so far (together with several excited cries of ‘Fuck me!’). An ever bigger one then greeted ‘My Iron Lung’ from 1995’s The Bends.

But of course, any thoughts that we were in for the traditional rock-show structure of new songs gradually giving way to an anthology of greatest hits were soon dispelled. From there, the new ones continued to crop up, while the old included plenty of the band’s more challenging tracks — especially the ones that overlay ballads with drumming that seems to belong to another song completely or that provide the kind of dance music designed not so much to make you tap your foot as stroke your chin.

These songs were all brilliantly, in fact thrillingly performed. Nonetheless, there were times when the whole gig felt like an extended tease, with Yorke himself in on our guilty secret — and almost daring us to wonder if, beneath our impeccable muso exteriors, we might quite like a little more old-fashioned showbiz. Only right at the end did he give us the mass singalong of ‘Paranoid Android’ from 1997’s OK Computer — and even then we sang along rather timidly, as if unsure that this was what Thom would have wanted.

All of which made for a classic Radiohead gig. By choosing songs from every period of their career, by playing them so stirringly and by staying uncompromising to the point of slight cussedness, they gave us an authentic expression both of their greatness and of that continuing strangeness. After all, there aren’t many bands who, had they gone for more obvious crowd-pleasing, would ultimately have pleased the crowd less.