British Sea Power, Czech Republic Embassy, London

It only takes one of these lads to change a light bulb

Is our least ordinary rock band on the brink, finally, of the big time? There's a feeling in the air tonight, as they play the UK's most Bohemian venue (literally), that British Sea Power might just make it.

To recap: BSP are the Cumbria-via-Brighton quartet with the name that sounds like a vintage history tome picked by chance from the shelves of a dusty bookshop, with a fondness for playing gigs in unusual venues (the Scilly Isles, the disused North Sea fort of Sealand), wearing First World War uniforms on stages bedecked with taxidermised fauna. Their pronouncements and interviews (famously, they once arranged to meet a journalist by giving an Ordnance Survey grid reference rather than an address) were endlessly intriguing, and the music was astounding.

Their debut album, The Decline of British Sea Power, ranged from Russian klezmer music to epic alt-rock, and if their second, Open Season, felt disappointing, it was only relative to its stunning predecessor. Third time around, with Do You Like Rock Music? – for which tonight's performance is a showcase – the timing feels perfect: the success of Arcade Fire and Franz Ferdinand has shown that there is a hunger for bands with brains and emotional breadth, and BSP have both by the shovel-full.

They know the traditional tricks of rock – swelling, rousing riffs and physically overpowering sonic overload – but use them to non-traditional ends. As well as elevating the heart, BSP expand the mind. One of their most treasurable aspects is the use of non-rock'*'roll words and phrases: "acetylene" and "allons-y" and "anti-aircraft". But there is meaning beyond the vocab: "Waving Flags", a commentary on pub culture and racism against Eastern Europeans, asks, "Are you of legal drinking age? On minimum wage? Well, welcome in ...."

The function room of a 1960s brutalist block in Bayswater is, for one night only, filled with competition winners in Dukla Prague away-kits and freeloading journalists lured by the free Budvars. The choice of location is not random. British Sea Power have many links with the Czech Republic, having often expressed an admiration for Czech literature, recorded an EP with Czech band The Ecstasy of St Theresa, and even thrown a party to celebrate the Czechs entry to the EU.

In front of numerous unexplained flags, they enter to "All in It", the new album's choral overture, and play a set that is often quite overwhelming.

Yan and Hamilton, the brothers who are the core of British Sea Power, share the same disturbed stare, as though they're slightly terrified by the gravitas of whatever they're singing about. There's little in the way of banter. BSP fans understand that.

One vignette captures the BSP rock/un-rock paradox. During their exhilarating finale, guitarist Noble is hoisted shoulder-high through the low-ceilinged room, and inadvertently breaks a light fitting. A courteous guest, he demands to be carried back in order to repair the damage.

If enough people make the correct equation between "unconventional" and "valuable", this could be British Sea Power's year.