So we’re sitting in Domino’s new offices, somewhere on an industrial estate in Wandsworth. There’s a train track outside one window, a gas holder outside the other, and some old Pavement and Sebadoh posters on the floor. Then there’s this massive crash of very heavy drums and guitars. The new Arctic Monkeys album has started, it seems.

This is “Brianstorm”, the first track and the first single from “Favourite Worst Nightmare”. My first thought is that Alex Turner hasn’t got any better at writing song titles. My second is that this is really, really good. I only hear the album once, and I’ve been over-excited at playbacks before – so apologies if the album turns out to be a stinker.

I don’t think it will, though. “Favourite Worst Nightmare” is a whole lot bigger-sounding than “Whatever People Say. . .”, but not in a lame stadium-wannabe way. It doesn’t feel bloated like so many follow-up albums by successful indie bands – the ropey new Kaiser Chiefs album being a case in point. Instead, it really is more ambitious, heavier – Jamie Cook’s guitar-playing resembles that of Josh Homme more than Carl Barat in many places – and with a fiercely bright production from James Ford, who did such a good job on The Klaxons’ debut.

There are certain similarities with that Klaxons record, in fact. It’s not a new rave album, by any stretch, but it feels more part of an art-rock lineage than in the blokerock tradition of Oasis et al. The funk influence is more pronounced, particularly in the bass playing of Nick O’Malley (much better than Andy Nicholson, on this evidence). Tracks like “D Is For Dangerous”, especially, are vaguely reminiscent of The Rapture finding a new terrace populism.

The opening few tracks are frantic, awkward and pretty uncompromising, and my potentially untrustworthy notes also describe them as a hybrid of Queens Of The Stone Age and The Specials. Then Track Five, “Fluorescent Adolescent”, ambles out, by some distance the catchiest song the Monkeys have ever recorded. From hereon in, the most notable influence is The Smiths, I think. Maybe the dreamy, elegiac Smiths of “Strangeways Here We Come”: there are some twanging, quasi-ambient backdrops to a couple of songs, and Turner’s voice has matured beautifully, crooning like Morrissey or Richard Hawley. Another track (Turner has explicitly asked we don’t write too much about specifically-named songs, and I’m happy to comply at this stage) reminds me a bit of “Girl Afraid”, though Turner is virtually rapping on it.

If you still want Turner to be a northern romantic, writing about Sheffield teenage life with a documentary precision, you may be disappointed. There’s little of that, and I suspect he thinks he’d be faking it to place himself back in that world. A lot of these songs seem to be about women, about temptation, about being desired – in a self-satirising rather than arrogant way, though. “Do the bad thing/ Take off your wedding ring,” goes one chorus. Turner’s melodies still have that wandering, made-up-as-he-goes-along charm. The heart of the Arctic Monkeys remains the same, it’s just the packaging that has got bigger and stranger.

“Favourite Worst Nightmare” feels, too, like a band asserting themselves. If Alex Turner was highlighted as some kind of street poet last year, it’s harder to separate him out from his bandmates: Cook, in particular, is rampant here. I’m trying not to get carried away, but today I like it even more than “Whatever People Say. . .” Now, if only I could hear it again. . .