Casting an appreciative glance around her Elizabethan environs, Gwenno introduces a song she says is about war crimes. “Or it could be about sitting on the Amalfi coast drinking a glass of red wine,” she reconsiders, playfully.

This conflicting interpretation – brought about because she sings in her two native languages, Welsh and Cornish – is at the heart of Gwenno’s music. Absconding from indie girl group the Pipettes, in 2014 she released her debut album, Y Dydd Olaf, a political, passionate exploration of media manipulation, revolution, patriarchy and cultural identity. For non-Welsh speakers, however, it’s breathtaking, sci-fi-influenced electropop that urges you to dance and dream.

Gwenno is joined by cello for this show – part of the Lauren Laverne-curated Wonder Women season – her high, otherworldly voice swooping above the mournful notes of Patriarchaeth before a synth beat kicks in. Swaying with her eyes closed, Gwenno’s lost in layers of synth, loops, samples and effects that subvert the sweet vocals and blissful pop melodies. The seductive groove of Nefolaidd is sabotaged by what sounds like rapid gunfire, the soft Lesley Gore-like sadness of Calon Peiriant is beset by mechanical whirring noises.

But the bass guitar, along with a sample of a profound-sounding speech by a young boy, is obliterated by synth shenanigans. And despite Gwenno’s appeal for her audience to “pull shapes”, they’re too busy admiring the music to dance. Still, it’s impossible not to get sucked into the reverent yet energised Cornish lament Amser. When Gwenno describes the night as “very surreal but beautiful”, she says it all.

• At Caught by the River Thames 2016, London, on 7 August (box office: 020-7736 3233) and Festival No 6 (0844 967 0002) in Portmeirion, Wales, on 1 September.