Always a pleasure to be taken by surprise. One of these four stars stands for the unexpected late-night treat of this satirical rock duo who are trending on BBC Radio 4's Now Show, but new to me, with strong lyrics, music and mocking, though not unserious, radicalism.

We might even change the world, suggests the ebullient Jonny Donahoe, who's like a cuddly Matt Lucas with bite and more hair. But they really do mean what they say, whether jumping into bed with UKIP for a "Farage a trois," standing up for soup, or diverting royal baby fervour into rejoicing once more (every Wednesday?) in Mrs Thatcher's memorial.

They sign off with a song about homosexuals not being allowed to give blood, recently banned by the BBC "because it promotes homosexuality." By then they've enjoined a chap in the front row to clear up his own beer spillage as a metaphor of industrial waste; wittily begged Scotland not to leave England in the lurch, ie with just Wales and Herefordshire for company; and got us all on our feet with a reprise of "God Exists."

Jonny's sidekick is a tall, gangly musician with a guitar who literally lets his hair down in a flaxen cascade at the end. They complement each other well and reveal the cleverness of their compilation in a summarising song that quotes all the others and redoubles their genuine claim to be frank, fresh, funny – and something completely different, even a contemporary Flanders and Swann.

Jonny & the Baptists: Bigger Than Judas continues at Pleasance Dome until 26 August (not 12)