The National, Royal Albert Hall, London

National treasures get my vote

I'm pretty sure you're not allowed to enjoy alternative rock if you're a Tory. (No, The Killers don't count.)

So the sombre mood that a gig by The National promised to cast on an election-night crowd contemplating a Conservative polls victory seemed somehow appropriate. Yet, while the election turned out disappointing for almost everyone, the mood of this show was unexpectedly euphoric.

Brooklyn-based but Ohio raised, The National formed in 1999 and released two albums before being signed by Beggars Banquet. Their first LP with the label was Alligator (2005), which included the likes of "Secret Meeting" and "Abel", still thrilling live staples. Next came 2007's Boxer, which ended up near the top of numerous best-of-year lists, and whose opener, "Fake Empire", found a place in Barack Obama's presidential campaign.

The Royal Albert Hall has a stunning sound system and enviable acoustics, but it doesn't exactly invite moshing. So it was an achievement for frontman Matt Berninger to persuade the seated crowd to jump to their feet early on with the opening "Stand up straight..." lyric from current single "Bloodbuzz Ohio", a suitably exhilarating comeback song from the fantastic new album, High Violet.

That said, the first few songs of the set were curiously flat. The instrument levels sounded a little skewed, while Berninger's voice needs time to warm up to optimum, black-coffee depth and richness. Despite his beguiling and distinctive bass timbre, he's more Bob Dylan than Barbra Streisand when it comes to hitting those plum notes. Only after an old song, "Baby We'll Be Fine", was abandoned midway (due to his forgetting the bulk of the lyrics), did the show burst into life with "Afraid of Everyone", a cut from the new album.

The rest of the band comprises two pairs of brothers. Bryce Dessner, who shares guitar duties with sibling Aaron, has a career beyond the band as the coming thing in classical, collaborating with the likes of Philip Glass and Steve Reich. Then there's bassist Scott and the brilliant Bryan Devendorf on drums, who provides not only structure to the songs, but shape and texture, too – especially in tempo-shifting tracks such as "Fake Empire", "Squalor Victoria" and "Slow Show", all from Boxer.

Another High Violet high point is also a home run with a London audience – the lovely, piano-led "England", which builds to a thumping, orchestral climax: "You must be somewhere in London," Berninger growls. "You must be loving your life in the rain." The singer's party piece is to disappear into the audience at the climax of each show, and he makes it a remarkably long way – all the way, in fact, to the boxes at the back of the stalls – still trailing his microphone cable behind him, mobbed by joyous fans.

The National's dark, brooding sound and "difficult" lyrics must explain why Vanity Fair this week called them "Brooklyn's answer to Radiohead". But like that band they can, too, be both exuberant and romantic. "I hope everything works out for everyone tomorrow morning," says Berninger at the show's close. That wish turns out to be optimistic – but so, curiously, do The National.