In just over a year, Clean Bandit have turned from classical crossover curio into ubiquitous pop phenomenon thanks to their breakthrough hit, Rather Be: it was streamed 32 million times during 2014, and recently won the Grammy for Best Dance Recording. But with their debut album not exactly proving a universal hit with critics, and a TV ad for a phone company raising eyebrows, it’s perhaps fitting that, for their biggest gig to date, the quartet have returned home to a venue that prides itself on being “the people’s palace”.

“I used to come here for ice-skating,” cellist Grace Chatto marvels, and the band never seem to shake off this sense of awe throughout their 90-minute set; while their string-laden, club classic-indebted sound fills the cavernous space, Clean Bandit never quite own it. Chatto is an ethereal presence, dressed in a black leotard with half a white maxi-skirt attached to the back; she plays electric percussion and cello, and provides some vocoder-treated vocals. Elisabeth Troy handles most of the singing, giving her all on the soulful Stronger and dancing up a storm with Neil Amin-Smith, who spends half the gig playing spine-tingling violin and the rest being Clean Bandits’ very own Bez.

The classical elements of songs such as Extraordinary and Mozart’s House are more pronounced live, and in the jazz-tinged Nightingale there’s a sense that Clean Bandit have pretensions of being Portishead. But they’re too busy borrowing remixer Jellybean Benitez’s 80s beats, judging by the new songs they play tonight, and for all their strobe lights and lasers, the band still only really have two hit singles and a cover of Robin S’s Show Me Love with which to try to bring this huge venue alive. Both Real Love and Rather Be are good fun, but it all feels like too much, too soon.

• At X Music festival, Edinburgh, 22-23 May; and Common People festival, Southampton, 24 May.