It had all started on a balmy Sunday night in London, with the few hundred lucky souls crammed into the live room at Hoxton Bar & Kitchen to celebrate 10 years of the shoegaze revival (and then some) label Sonic Cathedral treated to an euphoric warm-up set from the reformed Slowdive, the band at the vanguard of the shoegaze movement of the 1990s. It's apt that this was where they should re-enter the fray. Without Slowdive, Nathaniel Cramp would never have started Sonic Cathedral, but by the same token, without Cramp and his ever-excellent label, Slowdive probably wouldn't be back together, standing on stage playing an emotive opening salvo of the rousing 'Slowdive' and the spectral 'Avalyn', both from their debut EP on Creation, released over 23 years ago. Tears are shed. It's a hugely emotional moment for band and audience.

While Hoxton was joyous and intimate, the Village Underground gig feels like serious business – the start of Slowdive MK.2 proper and a 23-date jaunt around the globe. Maybe it's the austere brick building, with its vast ceiling (a literal sonic cathedral) or the increased audience size, but the mood is different. The goodwill can only flow once the first droning chord of 'Slowdive' is struck and the crowd realise that the band are match fit and raring to go. Typically, for a show of great import, there are early sound issues – Nick Chaplin is having problems with his bass guitar. "Can't you just plug it straight in?" enquires frontman Neil Halstead, still rocking the Dennis Wilson circa-Pacific Ocean Blue look, gesturing to the amp. Chaplin shakes his head.

"Even the bass player needs his pedals," jokes gossamer-voiced Rachel Goswell, who is doing her bit to reclaim the tambourine as the singer's instrument of choice from Liam Gallagher. While the difficulties are ironed out (the guitar tech is Kev from Seafood, indie fact-fans), Neil fills – not with the riff from 'Smoke On The Water', but with amiable chit-chat, plugging the Slowdive mugs available for purchase from the merch stall (manned by Erik from Deaf Center, ambient fact-fans). This easy repartee is symptomatic of how relaxed the band seem. Even when it's going wrong, they're not fazed. They are here, as Goswell promised when interviewed for The Quietus after the reformation was announced, to enjoy it. In fact, of them all, Rachel seems to be having the most fun, barely able to wipe the grin from her face. Peering into the audience, waving at friends and laughing when a fan shouts, "I LOVE YOU!" in a growl that makes it sound more like a threat than a term of endearment. But, regardless of what Richey Manic might have had you believe, this band do stir up strong emotions in people – and I'm not talking Mr Agreeable-type emotions, but feelings of L-O-V-E. Standing 3ft from me, there's even the obligatory indie gig circa-1992 snogging couple.

Issues resolved, they launch into 'Catch The Breeze' and there's a collective swoon. The sound still isn't spot on, but it's getting there, with Goswell adding her guitar to the mix, the band filling the building with a melodic maelstrom of glorious noise. From my vantage point, the band's second guitarist, Christian Savill, is just a head (bowed of course) above a speaker stack, but as he is the one who transformed the band's sound in the early days – from a jangly Primitives-style indie band – he deserves a mention.

The real revelations are not the classics, but the songs from Pygmalion, the band's third and final album; a series of austere ambient sketches recorded in isolation by Halstead and Goswell, none of which have been played live before the reunion shows. On record, 'Crazy for You' is a pleasant drift of a tune; here it is reborn – dynamic and punchy with an almost swaggering groove, Simon Scott pummelling his drums as Halstead and Goswell share delicious harmonies and the sound finally coalesces into a consummate whole. There's even a rhythmic middle-eight, where Halstead bashes out a beat on the body of his guitar, Goswell shakes what looks like maracas and the band get a serious groove on. Slowdive groovy? Whodathunkit?

'Blue Skied 'An Clear' is another Pygmalion number transformed from wafty ambience into a substantial song. Unfortunately it's also the moment when people choose to head for the bar and talk loudly – where I'm standing anyway – which is a shame because it is exquisite, with a breakdown where Chaplin hammers a chord like a metal worker in a forge. While the band aren't playing any unreleased material, these revamped numbers feel like new songs.

'Souvlaki Space Station' is greeted rapturously, a distant cousin to Ride's epic live favourite 'Nowhere', all dubbed-out guitars and a bassline from Halstead that could drill through a mountain. If that's a beast, 'When The Sun Hits' is an absolute monster, revealing the quiet/loud dynamic in all its glory. It seems strange to mention Led Zep in a Slowdive review, but the way Simon attacks his kit, and the thunderous drum sound produced, is reminiscent of the mighty Bonham. Fringes fly, fists pump, there's even a crowd surfer. They might not be the most rock & roll band on the planet, but for the duration of the riotous extended outro, the front of the crowd is a seething mosh pit.

The only way is down(er), but thankfully, Slowdive have some pearls in their armoury – the stately shoegaze par excellence one-two of 'Morningrise' and 'She Calls', from their second EP. The guitar sound is prime-MBV, churning, droning and the snogging couple take a break from locking lips to have a cuddle. They close with a cover of Syd Barrett's 'Golden Hair' with Goswell's haunting vocal crystal clear, the crowd chatterers enraptured and rendered mute.

The encore starts with a brave attempt to make the atmospheric 'Rutti', Pygmalion's minimal opener, into something more substantial, but it doesn't quite come off. A final bash through 'Alison', the band's most overtly pop moment, is welcome, but throwaway – to have closed on 'When The Sun Hits' would have left the crowd gagging for more. As it is, they just go gently into the night, sated. The band that was once the most reviled in Britain is now the most loved. It's about fucking time.