Encountering cult Brazilian Tropicália band Os Mutantes is like hearing your favourite 1960s groups (plus a few from the 1970s) passed through a steampunk blender. With their go-go beats, dreamy vocals, jump cuts and fuzz-guitar solos, they sound like a top 40 radio station from a parallel universe.

The original teenage trio of Sérgio Dias, Arnaldo Baptista and Rita Lee were like the Beatles, Stones, Beach Boys, Love and Jefferson Airplane rolled into one – but under the shadow of a military dictatorship. Os Mutantes never found the South American equivalent of George Martin, so their recordings didn't always hang together, and the sour political climate inhibited their development well before their 1970s demise.

Four decades on, it's another matter. The band is led by guitarist Dias, the only remaining founder member, but the seven-piece has a freshness and expertise that makes their complex songs – which lurch through rapid transitions, in the manner of albums such as the Beatles' Abbey Road or Freak Out! by the Mothers of Invention – sound easy. Dias beams throughout, delighted to be on stage with this material once more. I've seen that smile before: on the faces of the Zombies' Rod Argent and the Beach Boys' Brian Wilson when the latter's Smile was recreated in the same hall.

Dressed in gowns, capes and kaftans, the revitalised Os Mutantes march on stage to the grandiose, quasi-classical introduction to Dom Quixote and charge through a string of favourites, including Jorge Ben's A Minha Menina, which brings the crowd to its feet. Balada do Louco comes across like Hey Jude, while Ando Meio Desligado is as intoxicatingly psychedelic as Eight Miles High. They also play some beguiling new songs, including Querida Querida, from their 2009 album, Haih or Amortecedor.

In support were Porcas Borboletas – a Brazilian new-wave group with sharp musicianship, odd time signatures and a touch of Monty Python about them.