The last time Flo & Joan played Shepherd’s Bush Empire, they found a setlist on stage left by beloved indie-rock band the Feeling on the previous night. It made the sisters contemplate their own relationship to the music industry. Are Flo & Joan a proper band or doomed for ever to remain “musical comedy”? The problem with which, they deadpan here, is that “no one takes it seriously”. Cue this new show, its structure inspired by that chance discovery. Tonight, the duo play a suite of new songs that, title by title, matches the setlist of the band who preceded them four years ago.

And so goes the first half of With Feeling, which by turns delivers on and subverts that challenge – and proves handsomely entertaining either way. In the sisters’ hands, Fill My Little World becomes a neurotic number about the surfeit of stuff (cheap food, fast fashion, AI slop). Never Be Lonely returns to a favoured topic, Flo & Joan’s toxic co-dependency – with an added sight gag involving Joan (AKA Rosie Dempsey)’s questionable trumpet skills. Further numbers address the risks of poor punctuation and the need, in a society giddy on unfiltered self-expression, to “bring back shame”.

Elsewhere, those secondhand titles inspire bits of business or bad puns rather than whole new songs. That’s just as much fun: Flo & Joan are more expansive on stage than they used to be, amusing one another very infectiously as they navigate – via a wide array of musical styles, sibling backchat and surprise interventions – to the end of their setlist stunt.

Then comes act two, in which they unleash their rock band fantasies (leathers, bandanas, drumkit) on some well-loved numbers from their back catalogue: the one about social gaffes and the eternal cringe they engender (The Rest of My Life); the nonsense spoof folk song Lady In the Woods. As ever with Flo & Joan, you get richly wrought lyrical wit, sumptuous harmonies and musical surprises – this time with a droll top layer of bathetic rock posturing. A proper band, they may never be – for which, when improper is this much fun, we should all be grateful.

• On tour until 12 December