The title says it all. “Can’t Touch Us Now” declare Madness with breezy confidence, and the evidence comes loud and clear. It’s there in their history, in their achievements, in their canonical pop classics. It was there on the Glastonbury Pyramid Stage this summer, when the band blew away the cobwebs and the clouds with a sparkling greatest hits set that also shone with a couple of newies and a lovely David Bowie tribute in the shape of a heartfelt cover of Kooks.

“We were going to do All The Young Dudes but that a felt a bit pompous for us,” says frontman Suggs with typical self-awareness and self-deprecation.

And that untouchability was also in evidence at London’s Royal Hospital in August when Madness, in inimitable style – and really, literally no other band could have done this – unveiled their 12th studio album before a magnificent audience of Chelsea Pensioners. One British institution paying respect to another British institution.

Best of all, though, the proof of the unique status of Madness is there in the songs on that new album. Can’t Touch Us Now is the bold, lively, energetic sound of six writers, six lifelong friends, six Mad men playing at the peak of their powers.

“We made an early decision with regards to the way we’d record,” reflects drummer Dan “Woody” Woodgate. “And that was to get that energy back in. It was all about capturing momentum and speed, and get that excitement going.”

“We were all really pleased with The Liberty Of Norton Folgate,” says Suggs of the critically acclaimed 2009 album. It was a beautiful conceptual ode to a vanished London that set the seal on the ongoing vitality of a band whose “comeback” dated to 1992, when Madness reconvened after a six-year break. “We tried to work with different producers on Oui Oui Si Si Ja Ja Da Da, and ended up just going round and round the houses. So because we loved …Norton Folgate so much we thought: let’s just go back the same studio and the same producer.”

That producer was Liam Watson, pipe-smoking, lab coat-wearing curator-owner-builder of Toe Rag, the fantastically downhome and inventively rudimentary studio tucked into a quiet corner of Hackney (and, famously, birthplace of The White Stripes epochal Elephant album). He’s abetted by the band’s longstanding producer Clive Langer, while the album has been mixed by Brit Award winner Charlie Andrew (Alt-J).

“One of the advantages of working with Liam is that it’s only a 16-track studio so things happen very fast,” continues Suggs, noting that the album took a pacy three weeks to record. “We worked 11am to 6pm, no rock’n’roll hours, which is another good thing. You’re not sitting about getting pissed thinking how great you are. You just get it done, then you’re in again the next morning.

“The emphasis is what it was in the old days – on the writing and the rehearsing, not the recording. If you’re in a big technological studio you just spend most of your time farting around. You can’t fart around in Liam’s!” he laughs. “Push the faders up and there it is!”

First of all, though, Madness made sure the building blocks were properly in place.

“We found a place in Holloway, a little tiny rehearsal studio called Storm, 40 quid a day,” recounts guitarist Chris “Chrissy Boy” Foreman. “And we loved it. We didn’t need a crew or an onsite café or any of that nonsense. So we spent a lot of time last year rehearing and writing these songs. Then we did the Grandslam Madness tour, and I suggested we start playing these new songs live. That was a great process. It was really the band going back to what it was in 1979, all of us in a little room, writing songs and enjoying ourselves playing. That’s what we did almost 40 years ago when we started the band, in the basement of a house in Finchley Road that we could go to whenever we wanted. That was really, really important to our beginnings. It was the best nine quid a month we ever spent.”

With founder member Chas Smash having taken a solo album-pursuing leave of absence in 2014, the returning Los Palmas six found themselves creatively energised.

“As you get older you lose any fear, really,” offers bass player Mark “Bedders” Bedford. “You feel a lot more comfortable in yourself, which all of us in the band do. You press ahead and trust your instincts, which is a lot of what this record is about. It’s that thing of being out there on that voyage and not worrying what’s around you.”

That gung-ho spirit of adventure, not to mention a fine undertstanding of soul music’s historical sweet spots, is there in Mike Barson’s You Are My Everything.

“It’s quite an old song,” admits the pianist/keyboard player, “which I wrote on my own, about unconditional love, giving yourself in a relationship and not judging or expecting. We recorded it initially after Suggs left the band back in the Nineties. But we got in trouble not having a vocalist, and it degenerated into everybody singing their own songs. It all started to get a bit messy.

“But this time round,” he adds of a soaring, blue-eyed ballad featuring sublime backing vocals, “I was really pleased with how it came out. To my mind it’s Marvin Gaye meets Ian Dury in Isaac Hayes’ apartment. And I think Chris excels on the guitar – he really makes that track happen.”

Saxophonist and lyricist Lee Thompson explains how the instantly infectious title track, written with Foreman, began life as a lyric about Princess Diana, “and it also has undertones of the Tudor period, when there was a lot of unrest in royal circles”.

“Can’t Touch Us Now is a good illustration of what we’re trying to do,” adds Bedford. “It does hark back to the music we’ve always liked – it’s a bit Motown, it’s a bit Northern Soul. But it also goes back to Slade – it has that stomp about it.”

The pumping singalong that is Mumbo Jumbo, Thompson says, “is another political song. It was the banking crisis that sparked it off. It’s like Promises Promises on the 7 album [from 1981], about a marriage and the promises you make that are never kept – but it also applies to politicians. That said, I don’t know the ins and outs of politics – I leave that to Mike and Suggs to row about at the back of the tourbus…”

There’s a more personal, intimate slant on Blackbird. Foreman came up with the music, “an Otis Redding-type, old-soul tune”. Handed on to Suggs, this became a narratively rich, evocative tribute to Amy Winehouse. One set of north London legends, paying respect to another.

Then there’s the mighty first single, Mr Apples. It’s a Suggs composition that’s a classic Madness pop number, buoyed by punchy honky-tonk piano and a blessed with a brilliant unruly clatter.

“It’s a top Madness song,” agrees Bedford. “It’s the classic thing of having a jaunty melody, an up tune, with quite dark lyrics. These days you miss that clatter on records – it’s Pro-Tooled out. That was our thing making this album: we’re not going to worry about the odd slip. If it’s good take, let’s keep it, and let’s not iron out every kink.”

Describing the song’s protagonist, Suggs says: "Mr. Apples never stops. By day, a pillar of society; very clear on how people should behave; strict, moralistic, judgemental... But, when that old sun goes down, he’s heading off up the wrong side of town. Exhausting. We worry for him. He’s a very naughty boy.”

Coming soon, too, for this much-loved people’s band: more gigs, followed by more gigs. Having sold a whopping 220,000 concert tickets in 2015 – an “off” year, really – in 2016 Madness look set to top that tally if we factor in their self-curated September event House Of Common (on Clapham Common), November’s House Of Fun Weekender (in Minehead) and December’s arena tour of the UK.

“We do get different generations coming to our shows, most of whom know the classics because, I guess, they’re staples,” says Woodgate. “But when we’ve put in the new songs recently at festivals, they’ve gone down a storm – this summer they’ve been fist-pumping to one of the new tracks, Don’t Leave The Past Behind.”

“Touring now is great,” enthuses Suggs, “although it couldn’t be as exciting as it was on when we started out on the Two Tone Tour in ’79. You’re 18, going round the world with your mates, The Specials, The Selector, Dexy’s Midnight Runners…” he grins. “It was just a blur of hats flying in the air, pints going, legs and arms going up and down – and sulphate! Which I certainly can’t do any more,” chuckles this endlessly charismatic frontman. “But now I get on stage and look at an audience and think, ‘fuck, all these people have come to see us…’

“That energy we have onstage comes from a lot of things,” reflects this iconic band’s iconic singer. “Primarily we were friends first and foremost, and the band was a by-product of our friendship, not the other way round. And because we took that time out before the start of the Nineties, that was good for us.” These committed family men “inserted ourselves back into the normal world for a few years. Then, when we came back, the live thing exploded in such a great way for us.”

That said, he acknowledges that “we were getting drawn towards the black hole of that Eighties nostalgia, and then that’s when we set about writing …Norton Folgate. I just thought, if we can write one more great album before it ends, then we can say we made our best go at it. Then when that was critically acclaimed it gave us the warp factor to get away from that black hole.”

And now, by dint of hunger, and passion, and friendship, and a jawdropping way with a great tune and a smart lyric, Madness are out there, in a space of their own.

“The reason the album is called Can’t Touch Us Now is because we kinda feel we are alone, on our own journey” concludes Bedford. “We’re older, we’re not going to be in mainstream pop, and you could say we’re not regarded as a classic albums band. We’re just ploughing our own furrow and really enjoying it. So that title is Madness saying: we’ve made it this far by doing it our own way.”