Once was a time that The Columbia Hotel was it – London’s premier rock’n’roll roadhouse. If you were a band and you weren’t staying here, in the five converted regency townhouses on Hyde Park’s northern perimeter, you were either doing something very wrong or so very right that you no longer needed to take advantage of the hotel’s scrimper rates. At The Columbia breakfast started at 10am. Alcohol was served around the clock. Oasis were eventually banned for throwing glasses out of the window and onto cars below, one of which happened to belong to the hotel manager. But that kind of behaviour doesn’t go on here anymore, and hasn’t done for some years. London’s rock’n’roll hotel now, if indeed it still has one, is K West, a couple of miles down the road in the far less lustrous area of Shepherd’s Bush.

The Columbia inverted, K West looks like a moulded concrete Wreck Centre with a branch of Foxton’s installed in the ground floor. But inside it’s no nonsense modernity: glass tops and glacial, white space that tells you your bottle of beer is going to cost £6 even before Sir is presented his bill on a miniature silver dish. On Lancaster Gate, a little off white from decades of London fumes, The Columbia still looks magnificent and grand, its entrance beneath thick, thrusting pillars. Of course where K West combines a council estate facade with such a high-end, luxurious interior, The Columbia’s frontage can only ever disappoint once inside. Foxygen arrived here an hour ago from Paris, and as a Californian band so happily inspired by the music of the late 1960s it seems fitting that they should choose to stay in a place as out of time and out of taste as this.

We wait for the lift but it never comes, nor looks like it ever will – the LCD screen flickers as it tries to spell out floor numbers but it never quite manages to muster a decipherable digit. On the sweeping stairs (threadbare, tears patched by gaffer tape, but sweeping nonetheless) there is a huge vase full of dried flowers that have seen better days. They might not have started off dried, in fact. When we finally reach room 304, having managed to pass not one single hotel guest (a trend that will continue for our entire visit), I half expect to be greeted by a rotting woman in the bathtub. “Hey, I’m Rado,” says the wire-haired, band-on-the-road-thin young man who answers the door. “It’s a bit Shining here, isn’t it?”

Rado (first name Jonathan) is one half of Foxygen, one fifth when performing on stage. Drummer Sam introduces himself while Rado puts in a call to band singer and other one half/one fifth Sam France who soon bounds into the greying suite with bassist Justin and backing singer Lizzy. France is straight to our photo shoot, offering sunglasses on or off and the same with his vintage yeti jacket. Rado looks a little more ill at ease with this side of things but comes alive in interview mode. The pair, close since a very young age and surely no older than 22 now, occasionally bicker, as if they’re working on a full-blown Mick’n’Keef affair. No doubt they’d love that. Rado might just be the band’s musical genius, while France – blasé in conversation and a pantomime drug casualty on stage – is definitely the group’s showman. At New York showcase CMJ last year France emptied a can of Coke on Rado’s curls after calling him a hipster, something of a major slight in the Foxygen camp. Our interview takes place the following morning in the back of two black cabs and on two cold pavements as I tow France and Rado from one BBC obligation to the next.

“If I could be asked any question by an interviewer it would be, ‘can we not do this interview?’” As we leave The Columbia at 10am, just as breakfast is being served, I think, France’s less affable mood doesn’t last for long, although he does manage to get out: “I’d like to talk about things that are not music related.”

“I don’t have a problem talking about music to be honest,” says Rado. “I think the reason we talk about it so much is probably because of me.”

“The other day I remembered my earliest musical memory, which was driving through the desert from Las Vegas to California… I’m sorry, Sam, I’m talking too much,” he says, in an ‘I’m sorry if you’re too selfish to spend time with me’ kind of way. “… and we were listening to ‘Rumours’ by Fleetwood Mac in the car. Then I got into Blink 182 and pop and went off on all these weird areas and then came back to that. Now, my favourite thing in the world is ‘Rumours’.”

Rado stops and we both look at France.

“Oh. I just played on my uncle’s keyboard when I was little, that’s what I remember first. And listening to the Jurassic Park soundtrack.”

“I tried to watch The Lost World the other day,” says Rado, “but it was just Julianne Moore in ripped jeans falling over.”

“That one’s a little more violent,” says France, “a little more PG13.”

“A lot of Jurassic Park was animatronics,” Rado points out keenly. “E.T., too. That’s why I hate what Spielberg does now – he goes back in and fucks with E.T. and puts scenes in.”

What I want to talk about is ‘We Are the 21st Century Ambassadors of Peace & Magic’, Foxygen’s second album, depending on your definition, and one that’s as freewheeling and joyous as it sounds. On it, Foxygen (with an integral helping hand from producer and orchestral arranger Richard Swift) traverse and transform their heroes from the far-out end of the ’60s, from Bob Dylan to The Beatles to The Velvet Underground to The Rolling Stones, sometimes all within one song. It’s certainly the case on ‘No Destruction’, a steady country lilt that has France building to a cracked Jagger croak via Dylan sing-speak and a fleeting phrase delivered like Nico. ‘On Blue Mountain’ is all Jagger where France is concerned. You can almost hear his pout, even when the honky-tonk rushes and especially when blues breaks down. There’s Phil Spector’s right-hand-man Jack Nitzsche in the motorcycle instrumental ‘Bowling Trophies’, Serge Gainsbourg in lust letter ‘Shuggie’, The Zombies everywhere, The Modern Lovers in the drunken yabba-yabba of the title track and ‘A Day In A Life’ in the odder-than-a-dream, closing ‘Oh No 2’, which gladly nabs the endless piano, waking cries, dippy ‘Egg Man’ harmonies and similar stock footage to that of the Fab Four. Few songs end sounding anything like they did when they started, and when they do it’s after any number of tempo swerves, funk passages and/or the arrival of idyllic flutes and horns. Foxygen haven’t pinched from the greats one at a time but rather from all of them at once, and it’s worked due to their impressive competence. Bands like The Black Lips, Strange Boys and Thee Oh Seas are far simpler magpies, bashing out garage rock that sounds a little like ‘Get Off of My Cloud’ but not really. With far greater finesse, Foxygen have gone after far greater sounds of the ’60s, aiming more for ‘You Can’t Always Get What You Want’ and ‘Like A Rolling Stone’. Considering they so clearly are, though, Rado and France can’t seem to work out if they’re a ‘retro band’ or not. They contradict themselves and each other on the matter more than once.

“We’re not a retro band…” says Rado as we glide past the park.

“Well, we are,” France interrupts.

“Dude, we’ve moved from the most un-retro music, y’know? The music we were making when we were 16 was the most un-retro thing you’ve heard in your life. There was nothing ’60s about it – it was like rap music, just ridiculous. We’ve moved into this and it’s what we’re into now, and it’ll change again.” Rado makes his point, although when I later ask how they feel about being dogged with throwback slurs from others, France replies by saying, “We don’t care. We are a retro band,” to which Rado concedes, “Yeah, they’re not wrong about it.”

“I just don’t like when it’s a negative thing,” he continues, “when people think we’re being uninventive or just rehashing stuff because that’s not how it seems to us. I mean, that blog the fucking Quietus, the little pieces of shit, they’ve done four pieces on how much we suck, and that’s just too much hate.”

“Oh yeah, I’ve heard about this,” says France. “It’s become their thing – they just write about how much they hate us. It’s just wrong, man!” he laughs. “I was hoping it would seem so much like a ’60s album that it could be an album that actually came out in the ’60s, not a record from a new band that has a ’60s influence, because those bands wouldn’t really make sense in the ’60s.”

“It’s not an homage to the ’60s,” says Rado, “it’s a record we wanted to put out in the ’60s.”

The two members of Foxygen (a name coined by a friend who fancied a guy so much she said the ‘fox’ was her oxygen, or foxygen) met and grew up in Westlake Village, on the northern tip of Los Angeles. The success of ‘21^st Century…’ has them pegged as an overnight thrill, but they’ve been making music since 2005, and have already released a handful of EPs and one 7-track album – the much rougher, more wandering ‘Takes The Kids Off Broadway’. France says: “I think we’ve become slightly uncooler and slightly more popular. With the old album it’s kinda raw and cool, but for people who have an impression of Foxygen just coming into the new album, we might come off more like an MGMT pop thing. The new record is a properly produced thing, with pop hits, but it’s not cool.”

Rado describes their even earlier efforts as “strange little kid music. But it was really good for 15/16 year olds,” he says. “I mean, we were pushing ourselves really far.”

Pre-‘Kids Off Broadway’ Foxygen combined hot-potch musical elements that knew no snobbery, mixing “spacey” types like Beck and Flaming Lips with Willy Nelson slide guitar, amateur rapping and a lyrical obsession with aliens. Remnants can be found on ‘Kids Off Broadway’’s 10-minute centrepiece ‘Teenage Alien Blues’.

“I’m the most proud of ‘21^st Century…’,” says Rado. “I think it’s our best songwriting, and then ‘Take The Kids Off Broadway’ is really close to my heart, and then all the records we made as kids too. But yeah, if you’re just coming into this now, it might seem that we’ve not been doing this for ten years.”

“Yeah,” says France, “it’s like, ‘who are these idiots? Oh great, they’re rehashing ’60s pop. They look like two fucking idiots!’”

As France and Rado enrolled in two different colleges, they kept Foxygen going in the holidays. France also played in a “kooky funk band” while Rado “played hired piano for the worst singer/songwriter, like, the worst music you could hear in any coffee shop ever!”

The rumour – started by the band, it turns out – goes that Rado was a child prodigy of the classical world circuit.

“Sam, are we going to keep going with this one or…”

“Dude, this is not my thing.”

“Well, it was,” insists Rado. You started it.”

“I started it but you kept going with it.”

“Ok, what happened was…”

“In the last interview that we had I think Rado said that he used to play classical music and the interviewer kept asking about it and Rado was just making up these lies,” say France as he peers out of the taxi window.

“Yeah, people keep asking me about it so I have to keep going further with it,” Rado nods. “The story now is that I was classically trained and my parents made me play all of these different instruments – like tuba and trumpet and every instrument of the orchestra – and then I would perform at these sold out concerts all around the world…”

“And then your babysitter pushed you out of a window and you hit your head and now you can’t play classical music,” says France. “That’s what he had to say to keep my lie going, but it’s just terrible lying about this. It’s useless, a waste of time.”