"We saw Noel Gallagher the other day! Backstage, at a festival. We were introduced to him, very briefly, and as he walked off, he said, "All Ways? What, like the shampoo?"

Incorporating Manchester's rich musical heritage into your stage banter is a well-worn and ultimately risky move for international bands playing there, and Molly Rankin already knows it. The last time Alvvays were in town - a few hundred yards away at the much smaller, much hipper Deaf Institute - she announced that her first Gallagher record was Heathen Chemistry, to painful silence; in the land of the hipster, there's apparently no hierarchy when it comes to the relative coolness of Oasis albums.

That kind of frosty reception is by no means a rarity, either. Salford Lads Club is usually the first port of call for bands from North America, with the obligatory Instagram shot the Mancunian equivalent of a photo with a koala bear in Australia, or a moody black-and-white of the Manhattan skyline when a giddy group reaches New York for the first time. It's an approach usually at odds with Manchester's predisposition for sardonic self-deprecation; I remember, for instance, Jenny Lewis and Johnathan Rice playing a show in town a few years ago. "Our guitarist has a tattoo of a Manchester musician!" beamed Lewis, as if by bringing him along, she had guaranteed her own ascension to the city's hallowed inner circle. "Can anybody guess who it is?" A veritable parade of piss-taking ensued. Simply Red? M People? "Um...it's actually Morrissey," she revealed, perplexed. The boos rained down, as we anxiously sought to distance ourselves from the illustrious self-character assassin and occasional singer. This is one of a great many examples I could serve up along these lines.

Alvvays' biggest gig in town to date, though, doesn't rank amongst them. They're at the tail end of an extensive UK jaunt - you know, the kind that hits the likes of York and Cardiff as well as the usual stops - and there's nothing but warmth emanating between stage and floor and back again in a room three times the size of the last one they played, eight months previous. They filled plenty of prominent festival slots a long way from home this summer; the John Peel stage at Glastonbury stands out, as does an appearance at the sharp end of the bill on Reading and Leeds' Festival Republic stages. Only a year previous, when they released their self-titled debut, Rankin was taking time out from her waitressing job at a Toronto pizzeria to speak to national outlets in Canada. They seem to have come a long way, fast.

Backstage after the Manchester show, Rankin herself isn't so sure. "It's escalated, sure," she says, "but in a really gradual way. It kept building really slowly. I think it was when the year-end list stuff started to come out - which, let's be honest, tends to be in the fall - that we started to become more visible. It was weird, because I'm usually ignorant to all that stuff, but suddenly we were surfacing in places we had no connection to; music papers and blogs that hadn't covered us before. When that started it was, "oh, really?", but it was the start of this progression towards bigger things. You'd spot these little moments, like the support we were getting from 6 Music over here. It's been a joy, really."

Rankin is the primary creative force behind Alvvays; the band grew out of a slew of songs that she'd initially written to record under her own name, and she had the razor-sharp wit of the lyrics and melodic jangle of the guitars down well before the project developed into something less autonomous. All five members of the group grew up a long way away from any recognisable music scene, though, and before the ubiquity of the internet broadened her horizons, Rankin spent a long time isolated from the bands she'd go on to take her cues from.

"I'd listen to what was on the radio, and call in and request songs, but that was pretty much it for a while, until we had MuchMusic and Napster," she recalls of her upbringing on Cape Breton Island. "Alec (O'Hanley, guitar) grew up nearby on Prince Edward Island, and I guess they had a record store, but if I wanted to buy a CD, it was something like a forty minute drive to the nearest Wal-Mart. And, you know, I was twelve, so I couldn't do that on my own."

"It wasn't until I was twenty-one that I was getting into The Smiths and The Replacements, and even then, I'm still listening to albums like Viva La Vida and thinking, "wow, this song's a lot heavier and more shoegazey than the stuff they've done before." I wouldn't even have known what 'shoegaze' meant, but I'd say something like that to somebody and they'd go, "oh yeah, you should check out My Bloody Valentine." I still feel like I'm working my way backwards, even now."

In Manchester, he band are a long way from their geographic roots, but there's still a powerful sense of homecoming; Johnny Marr's signature approach to six-string harmonics looms large over their album, but the knock-on effect that the city's biggest names had was pivotal, too. "I think the first record comes out like a mix of The Smiths and Kathleen Edwards," says Rankin, "but, you know, Oasis were important to me. They were a total gateway band; before the internet, how would I ever know about The Stone Roses in Cape Breton, in Nova Scotia? That's why I brought them up tonight; it's OK to pay tribute to people who contributed to the whole of pop music, who have some integrity. We were watching Limp Bizkit at Reading, and the tent was packed! That's fun, but you see that and then throw out Noel Gallagher's name, and the reaction's extremely polar. It's weird. I guess it's partly because of his persona, but I don't think he takes himself too seriously. Maybe Liam does, though."

The influences that look set to drive the sophomore Alvvays full-length are considerably more obscure; "we've been listening to a lot of The B-52s, The Shop Assistants, Dolly Mixture, and Television Personalities." What's evident from the handful of new cuts that have made recent sets, though - 'New Haircut', 'Your Type' and 'Hey' among them - is that a faster, bouncier and more upbeat feel is likely to permeate the next record. "I think I fed into the sad part of my brain a little too much last time," Rankin admits. "I don't want this one to be as sombre. I was in a very isolated place when I was writing a lot of those songs; I was living alone, and it seemed like all my friends were off on tour whilst I was waiting tables through the winter, on this crazy island that was under six feet of snow the whole time. I'm in a very different mental space now, I think - I can't get away from anyone! - but I'm never not self-conscious about being too cheesy or too hard on myself."

There's a balance to be struck, though; part of what seemed to attract people to Alvvays was a penchant for downbeat introspection. They play the album's stormy closer, 'Red Planet', during tonight's encore - just Rankin and a backing track - and it sparked an out-and-out singalong. "That was really cute! And welcome, too, because I've been slowly losing my voice these past few shows. There's definitely a consistently good reaction to the slow ones, for sure; 'Ones Who Love You' and 'Party Police', those songs are sad ballads, you know, and people seem to love them. I think depression is a big part of it; being open about it, people can draw something from that."

If anything's going to bridge Alvvays and its follow-up, it'll be the band's genuine love of classic pop songwriting. On this last run, they've covered British classics past and present; Camera Obscura's peerless 'Lloyd, I'm Ready to Be Heartbroken' has made a smattering of appearances, as has 'He's On the Beach', one of countless gems bequeathed to us by one of the most sorely underrated minds in pop - Kirsty MacColl. "I remember Alec was playing in a power pop band when I first met him, and this guy who was producing them loved Kirsty MacColl. I think he played me 'A New England', and I was thinking, "who is this? It's like The Smiths, but there's a girl singing!" I bought Kite, and that was that. 'He's on the Beach' is one we all really like, and it feels like we've been playing it forever. I hope it's not blasphemous to do it over here; she was such a beautiful creature, and there's something so mystical about her legacy - the way she left us so tragically, and the way all these amazing figures speak about her."

The band's show at Shepherd's Bush Empire - their biggest in the UK to date - effectively brought the curtain down on touring for their first album, save for a handful of dates in back home before Christmas and in Australia shortly afterwards. With a slew of demos already laid down for LP2 - "we moved our tape machine to the basement, so we can record at 3am without any collateral damage" - a degree of urgency is already beginning to creep in, even if there's little in the way of label pressure. "I would like to be done with everything by the end of February, and that includes the record. We've been trying to bring the touring to an end for a while; Alec and I aren't old, but we're not twenty-one anymore either, and we're getting to the point where we're understanding the power of the word no. Last time, I had to quit my job to finish the writing; I had to stop working at Smoothie Hut, or wherever, so I could work on the later tracks, like 'Adult Diversion' and 'Next of Kin'. I'll probably do that again, and everybody else will go back to their day jobs for a little bit. It's just me who can't do it. I struggle with the whole thing of "oh, I've got to turn up fifteen minute early for my bussing shift", you know? I guess I don't really have my priorities in order..."

Alvvays is available now via Transgressive.