Thom Yorke, Corn Exchange, Cambridge

Despite being one of the most prominent activists in music, backing a specific party has never really been Thom Yorke's style. Therefore, it is something of a coup for Tony Juniper, the Green Party's prospective parliamentary candidate for Cambridge, to persuade his friend to perform this benefit gig for his election campaign.

At the risk of being accused of stereotyping, it is likely that a lot of Radiohead enthusiasts will be sympathetic to the party's environmental values, but in all honesty this rare acoustic concert by Yorke could have been a fundraiser for Ukip and throngs of dedicated fans would have still descended upon the Corn Exchange in Cambridge.

Thankfully, politics does not dominate the evening, at least after an introduction from Juniper. This is no political rally – the crowd are there for one man and one man only, and from the moment Yorke begins with "The Clock" they are reverentially quiet. At an acoustic gig such as tonight, this can make more of a difference than one might suspect – there are almost none of the idiotic whoops or background chatter that can often ruin such concerts.

Yorke himself is as relaxed as the audience is respectful. The singer has always had a reputation for being rather awkward, but in the past few years he has seemed to loosen up, and tonight is no different. "It's all right, he likes being in bed," Yorke jokes, when the crowd respond sympathetically after he tells them bandmate Jonny Greenwood is unwell, and when he trips up during the tricky keyboard riff of "Weird Fishes/Arpeggi", he merely giggles and carries on playing.

No Radiohead fan ever expects a greatest-hits set, and Yorke uses the opportunity to introduce a number of his own new songs. One – titled "The Daily Mail" – is dedicated to the "open-minded, liberal people of our country", but more impressive is the haunting "Give Up the Ghost", in which he loops his own voice.

Just as interesting is the way he reinterprets tracks from The Eraser, his one solo album so far, which was released in 2006, largely stripping them of the electronic beats that dominated the record. This is most effective on the title track from the album, which becomes much more vulnerable when Yorke's voice is accompanied just by the piano, while the electric bass of "Harrowdown Hill" is brought to the fore.

Of the Radiohead songs of the night, most are taken from the later stages of the band's catalogue – save "Airbag" from 1997's OK Computer – although such is the constant forward drive of the band that songs performed tonight such as "Pyramid Song" and "Like Spinning Plates" that were once seen as part of strange new directions for the band are now regarded as established classics. Judging by the performance tonight, the spellbinding "Videotape" from their last album, In Rainbows, will soon be considered part of that category too.

That Yorke finishes on "True Love Waits", an old favourite that has never been released in studio form, is fitting considering the number of Radiohead aficionados in attendance. Nonetheless, with him about to embark on a tour with his new band – the freshly named Atoms for Peace (featuring a certain bassist called Flea) – and Radiohead reportedly working on their latest record, as always with Yorke the next step continues to look as exciting as ever.