The Horrors, Academy, Oxford Lianne La Havas, The Social, London

This band is now so good that our critic is prepared to put its background of privilege to one side; plus, a new soulstress

It would have been all too easy for The Horrors to spend the late Noughties the rock'n'roll way – shagging and snorting a path through Shoreditch, feasting on impressionable fresher flesh, cashing in on their youth, hipness and sexiness till they maxed it out. Instead, they somehow found the time to do the decent thing: they actually got better.

There's one, and only one reason to feel any bristling resistance towards The Horrors, and it is social class. That infamous Telegraph property article in which Tom Cowan's art-dealer mother spoke about simply giving a Fulham flat to the future Horror (and his brother Freddie, of The Vaccines) will live long in the memory. The impression of Little Lord Fauntleroys playing make-believe that they're Screaming Lord Sutches is a hard one to shake.

The surefire way of forcing a posh-boy camel through the eye of this critical needle is "being any good". The Horrors have managed that not once, but twice. I'll always miss the band The Horrors used to be: the excitement, the massive hair and the unruly chaos of their garage-goth phase. For me, their achievement in ditching Sixties garage and embracing Krautrock on their second album, Primary Colours, has been overstated and overrated. Third time around, however, on Skying – one of the albums of 2011 – they absolutely nailed it.

The sound The Horrors are making at the moment is mighty: a monumental fusion of the oceanic rock of 1988 and the "big music" of 1984, the arrogant grandeur of Psychedelic Furs and mid-shark-jump Simple Minds (The Horrors are playing with fire by drawing on the Sparkle in the Rain era rather than the earlier, cooler stuff) combined with the piledriver puissance of My Bloody Valentine. At other times, I find myself thinking of The Cardiacs circa "Is This the Life?" and The Cure circa Disintegration.

The snowblinding synths of "Scarlet Fields" show just how much the keyboards – merely a kitschy period accessory in the days of debut album Strange House – have come to the fore. It's no coincidence that it's a sustained synthesiser chord which is left to hang in the air after "Still Life", bridging the gap between main set and encore.

I overhear someone complain that "They haven't got their spark tonight", but there's such a thing as too much spark: according to a news report on the NME website, singer Faris Badwan is in trouble for allegedly punching a fan during the Liverpool show a couple of days earlier. In any case, they make up for the absence of physical violence in other ways. Midway through the final encore "Moving Further Away", the nine-minute epic which forms the centrepiece of Skying, they work up a genuinely startling electrical storm, guitarist Joshua Hayward falling to his knees in front of the monitor wedge, the better to coax wave after wave of obliterating, ear-scouring noise from the PA.

Right now, there can't be many bands who can match The Horrors for sheer, awe-inspiring majesty. They leave without playing even one song from their original incarnation, making the gothic pixie boot depicted on the "I Am A Horror" T-shirts at the merch stall seem utterly anachronistic. The Horrors' transformation is now complete, and it is astounding.

The music industry invariably operates using Partridge logic: if a particular act makes it big, the response is, "People like them, let's make more of them". With Amy no longer with us and Adele currently too croaky to perform, there's a new wave of vintage-sounding soulstresses about to break. The anointed ones this time around include the Critic's Choice Brit-winning Emeli Sandé (of whom, more next week) and, as flagged up by the BBC Sound of 2012 longlist, Lianne La Havas.

Catching a glimpse of La Havas at the opening night of her sold-out Social residency isn't easy: craning my neck from the lobby, I can just about make out that when she straps on something called "Colin, my pride and joy", it's a guitar.

With her retro side-bun and Dionne Warwick-esque vocals, La Havas ticks all the tasteful boxes, and while her sound – simple piano motifs, gently brushed drums, guitars plucked in a laid-back, Latin manner – may err on the side of Later with Jools Holland-friendliness, there's a definite life-of-the-mind going on underneath that hairdo.

The 22-year-old Londoner's smartly observed songs deal with self-loathing ("You've broken me, and truly taught me to hate myself"), cinematic romance ("Take our positions as the cameras roll /You be the guy, I'll be the girl ...") and generation-gap love affairs ("Is it a problem if he's old/As long as he does exactly what he's told?"). And her closing cover of Jill Scott's "He Loves Me" proves that the oh-so-tasteful Lianne has plenty of taste herself.

Next Week

Simon Price catches an award-winning double bill of Emeli Sandé and Michael Kiwanuka

Pop Choice

Motown legends Martha Reeves and the Vandellas, with over a dozen Sixties soul smash hits up their sleeves, play a residency at Ronnie Scott's in London (Mon-Fri). Meanwhile, Madness main man Suggs takes his My Life Story evening of words and music to the Churchill Theatre, Bromley (Mon) and Palace Theatre, Southend (Wed).