You could never accuse Arctic Monkeys of making anything easy for themselves.

Their debut album Whatever People Say I Am, That’s What I’m Not, topped every end-of-year poll going, and became the fastest-selling debut in British chart history. Those are just the facts. But revolutions are about more than mere facts; and this rewired a generation, broke the boundaries between the moshpit and the dancefloor, invalidated the whole concept of celebrity culture to become that rarest of things, a smash hit with its soul intact. Most bands take years to whip up that sort of acclaim.

How could even these four talented young men hope to follow that? Forgive us for stating the obvious, but you go and make a better one. Arctic Monkeys had actually started work on ‘WPSIA,TWIN’ with Simian Mobile Disc's James Ford and Mike Crossey, before they'd really become producers du jour, but for one reason or another, the sessions were abandoned and the job was completed by Jim Abiss. But sensing kindred spirits – and with a renewed sense of confidence in their instincts after everything went so spectacularly right first time – they returned to their old mentors, whose star had risen in line with their own over the previous two years. "I think it was very obvious from when we did that first session that it was sound with them,” affirms Alex, "they understood it." "And," adds Jamie, "they're not much older than us really."

After locking themselves away from the world first time round, the band decided to record in Miloco Studios in Shoreditch, East London, "getting all new rave in East London," says Matt, slyly. The experience saw them embrace full flow of the city, going out, living life and even having a bit of a party. "I think you can really hear it in the snare sound!" jokes Matt, but he’s closer to the truth than he thinks.

The other big change within the ranks of Arctic Monkeys was the introduction of old friend Nick O’Malley on bass halfway through last year. This, too, was taken in everybody’s stride. "I’d known them all since I was 10 years old," says Nick of his new bandmates. "We've all lived in the same area, so it wasn’t like coming into a band where I didn’t know what they’d be like. It's just been a laugh really, it’s been fine."

So with the numbers back up, it’s time for Act 2. 'Favourite Worst Nightmare' is everything you hoped Arctic Monkeys would do next. Not so much a sequel as an upgrade, a breakneck technicolour journey through screwball punk and guitar-fuelled dancefloor heroics, it's very, very fast and very, very loud; a brilliant racket that proves there’s infinitely more to Arctic Monkeys than writing pretty little ditties. Yet at the same time boasting some of the strongest songs they’ve ever written.

Musically at least, it follows on from the last songs they wrote from ‘Whatever…’; ‘View From The Afternoon’, ‘From The Ritz To The Rubble’ and ‘Vampires’. A fast and throbbing record was always part of the plan. They did have slow songs, but as Alex points out, “they were never as much fun in the rehearsal room or whatever so why do them? I’d rather make an album like that that’s exciting. I don’t really want to make it sound like we’ve ‘grown up'."

There’s little danger of that, with the band being only exactly a year older than they were when they made the first one. But they’ve seen a lot of the world in that time, seen things neither you or I could ever believe. And no, they haven’t gone and made a fame record, having done an admirable job of avoiding that particular circus. It doesn’t quite tell the stories of riot vans and High Green undesirables. As Alex points out, “we still do a lot of the same things. We just do them in different countries.”

And Alex’s razorsharp-wit is on tantalising form. Take Brian, the flash, insufferable anti-hero of Morricone-gone-drill’n’bass opening shot ‘Brianstorm’. Whether through bad memory or good manners, they won’t reveal his true identity, but scummy men, it seems, come in all shapes and sizes. Alex remembers: “What happened were we met this guy, and when he left the room we were a bit freaked out by his presence, so we did like a brainstorm for what he was like, drew a little picture and wrote things about him.”

"He was right weird," shudders Jamie Cook. "He just appeared with, like, a business card…” “… and like a round neck T-shirt and a tie loosely round it, I’d never seen that before. It felt like he were trying to get inside your mind. We were checking out his attire, freaked out. He definitely left a mark on us. He might have been a magician. He might even be here now. But if we ever found out who he was, it might spoil it.”

And despite how far you go, the songs have found that life’s quibbles don’t really change wherever you go. ‘D Is For Dangerous’ – the source of the line ‘Favourite Worst Nightmare’ itself – is a typically colourful tale of 'dirty little herberts' and their sexual politics where insecurity is no barrier to promiscuity, of “desperately trying to recreate what was only three quarters of an hour ago.” The prickly ‘Balaclava’, meanwhile finds that the innocent punch-ups of ‘Riot Van’ have given way to something more sinister.

Elsewhere, Alex lets the listener deeper into his own soul. The album’s pop centrepiece ‘Fluorescent Adolescent’ talks sharply of fishnets and boy-slags and ‘little books of sextips’ and remembering ‘when you used to be a rascal’. It’s the story of “somebody that once you thought was amazing, and turns out not to be.” And what started as “a pisstake song we were just having a laugh with,” has turned into a bigger tune than you could ever imagine. A disco-inflected cousin of ‘Mardy Bum’ with ‘Festival Anthem of 2007’ tattooed all over it in gaudy pink and green.

Still intact is Alex’s knack of spinning magic out of the mundane. Emotional centre ‘The Only Ones Who Know’ sounds like the tenderest song of longing; but, insists Alex it dates back to an innocuous story of two newcomers to the city one Fresher’s Week. "There was this girl and this lad, who had obviously been lumped together, and they just asked us, it was like Sunday night, ‘where’s good to go to tonight?’ I wrote that about them."

But such a simple request for directions stirred a romantic spirit in Alex, who, hoping they would be ‘holding hands by New Year’s Eve’ made it ‘harder to believe that true romance can’t be achieved these days’." Maybe they’ve got married by now. Then there’s the “goodbye songs,” the energetic Wizard-of-Oz fairytale ‘Old Yellow Bricks’ (“Dorothy was right though”) and the plaintive ‘505’. Perhaps their most daring work yet, it weaves golden swathes of spidery guitar around a plaintive Alex, winding his way through hotel corridors, crooning in anticipation of the adventures ahead. But more of those on the next album.

But if Favourite Worst Nightmare belongs to anybody it’s the band themselves – all four of them this time – not just the funny one who writes songs about girls on dancefloors. From ‘This House Is A Circus’ supercharged waltz, the blink-and-you’ll-miss-it Duran Duran reference in tribute to ‘Dancefloor’ to the dense prog (yes, prog) of the stultifying ‘If You Were There, Beware’ (which begins like the end of ‘Vampires’ then only gets madder), it’s the sound of four men gorging themselves on musical possibility, informed as much by (off the top of their heads), Prodigy, ESG, Shocking Blue and Release The Beast as any of their indie comrades. “Thinking of the music we’ve heard since we made the first record,” says Alex, “we’d heard fuck all really.”

Next up, recreating such fast and furious songs live is going to test every fibre of their being (Matt has even taken up boxing to have any hope of surviving the tours), but with barely a moment to catch their breath, the Arctic Monkeys are ready for action. Again. How do you follow up one of the most adored albums of all time? Simple. You make an even better one. No-one ever said it was going to be easy.