The Postbahnhof is one of those wonderful post-industrial venues that it would be lunacy to tart up too much.

Glasgow has a few of those (and some of them have been), but it is in Berlin that they seem perfectly placed. The former Eastern portion of the city may now have venues like the O2 World arena that are of a style very familiar to Western gig-goers, but it is the wide and often suprisingly empty boulevards and monumental architecture that still gives the place an alien atmosphere.

The Postbahnhof was once an adjunct to the (still very much operative) Ostbahnhof railway station, and mail trains could be driven right into the sorting office where bags of letters and packages would be hooked out of the trucks and shuttled along overhead rails that mirrored the tracks below. Much of this infrastructure can still be seen, although the link to the East's passenger hub has been severed, and the reclaimed artspace includes vast curved halls and wide external staircases, as well as bars and auditoria of various sizes with a suite of offices, dressing rooms and kitchen facilities on a floor above.

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When I arrive, hotfoot from the S-bahn link to the airport, the plan that I have an early allocation of face-time with my quarry has already crumbled to dust. In the largest of the dressing rooms, the entire nine-piece Paolo Nutini touring band, who may still sometimes be referred to as The Vipers, are working up a new, mostly unplugged version of his upcoming single Scream (Funk My Life Up) to play for the video cameras of Rolling Stone magazine's website in a hastily set-up corridor location in under an hour's time.

It's deja vu all over again, as baseball's Yogi Berra once famously remarked. On an earlier excursion in my acquaintance with the Paisley-born singer and songwriter, I arrived at a similar hour backstage at Blackpool's Empress Ballroom to find that any hopes of an early interview had been stymied by the sudden need for Nutini to learn the more beautiful original tune for Auld Lang Syne so that he could perform it with Phil Cunningham in a pub in Lytham St Annes for a forthcoming BBC series, Scotland's Music.

I helped by finding, on iTunes, a lovely recording of it I knew by Scots duo The Cast, from which Nutini's regular bass player Michael McDaid worked out the chords. The pub in Lytham had been decked out in tartan like it was Hogmanay (it was April), and peopled with local ex-pats like former footballer Colin Hendry, many in kilts. After Paolo had chatted, sung and chinked whisky glasses with Phil, he went back to Blackpool and told a packed hall of excited girls about his New Shoes.

The Berlin experience would never become quite as surreal as that, but the parallels were striking. Just as, in 2007, the 20-year-old Nutini had decided on the eve of the BBC recording that only the rare original melody for Auld Lang Syne would be right for his appearance on Cunningham's series, so, with barely enough time to make it happen, the 27-year-old band-leader had changed the plan to perform an acoustic cover version (possibly an Arcade Fire tune; afterwards no-one seemed entirely clear) and asked his musicians to help him make a very different version of a song that had previously been a studio-created beat-heavy slice of dancefloor funk.

The main difference is that where once it was a question of learning just the simple essence of the song, now a collective of 10 very fine musicians are working in consort to create the arrangement. It is an organic creation that echoes the way much of Nutini's new album has come together in the five years since Sunny Side Up, his follow-up to debut These Streets. From the kitchen next door, I hear the new version take shape as keyboards, horns and backing vocals are added, then we all troop downstairs to where the filmmakers have set up and the new arrangement is delivered, in two swift takes, for the Rolling Stone cameras. This exclusive will be used as part of the celebrations of the magazine's 20th anniversary in Germany and, as the last chord fades away, Nutini turns to the lens and, with a come-hither look, deadpans "Happy Birthday, Rolling Stone" like Marilyn Monroe at Madison Square Garden.

In fact it was at New York's Carnegie Hall that I first saw Nutini command a vast theatre. The occasion was a New York Pops concert at which the guest of honour was Atlantic Records co-founder Ahmet Ertegun. As the label's latest signing, Nutini was taking the stage in the company of a diverse bill that included Liza Minelli, Kid Rock and the cast of then-new musical Jersey Boys. Not only did the teenager hold his own in such august company, it was also clear at the reception afterwards that Ertegun was a sincere admirer of his young talent. After the label boss died at the end of 2006, it was only appropriate that Nutini was on the bill alongside Led Zeppelin in the UK tribute concert to him at London's O2 Arena.

The Postbahnhof is another sort of gig altogether, but it suits the soul review sound that Nutini is clearly aiming for with his live band. The concert has been upgraded to a larger space within the venue complex and, over the next few weeks, new dates will be added to an ever-lengthening schedule at ever-upsizing venues. A T in the Park Scottish festival date is only the first to be revealed of a full summer that will seen Nutini and his band visit most of the continents of the world and (I'll stick my neck out) pretty much all the festivals you have heard of, as well as a good few better known to music fans in Korea and Mexico. An extension of his management team to include a chap whose other charges include Arctic Monkeys is aimed at growing Nutini's international standing.

Remarkably, though, the Berlin date is the first time the group has played together for a proper paying audience in years, and a debut for this particular line-up. An industry and fan-club members launch event had unveiled the new music that makes up the bulk of the set just three weeks previously at the Boston Arms in North London. Since he stopped touring the material from 2009's Sunny Side Up, Nutini has been hopping round the globe, recording bits and pieces of music, some of which will be found on Caustic Love, the album that is released on April 14.

As the new material is played for audiences in hip smaller venues in Berlin, Amsterdam and Paris, the precise shape of the new album is still coming together, with tracks being added as final mixes are approved and some samples appropriated for the recording clear legal hurdles. Yet although everyone concedes he can be exasperating, no-one in Team Nutini is biting their nails. That's they way things are with Paolo: you either go with the flow until a deadline become unignorable or you suffer the anxiety alone. Whatever is planned, things may well change, right up to the last minute.

Following Ertegun's lead, Atlantic have kept faith with their signing, and although the relationship has not been without its tensions, particularly in the run-up to the completion of Sunny Side Up. But after the success of that album, Nutini has been allowed the time to work through to a new set that he is happy to release on to the market, and promote with the enthusiasm he knows is required.

"It has been a big expressive journey," he tells me between a somewhat curtailed soundcheck with which the frontman was less than entirely happy, and the show that night, "with its compromises and restrictions. But it is down to me in the end, and I have to learn to live with it and let it go. I have never been working for people who put the screws on you, but don't get me wrong, people would say: 'You've got to finish the record.' But I've been around long enough to see when pressure is real and when it is manufactured. My music has made them money and so I get heard."

That applies to the live line-up as well. There are few young singer-songwriters who commit to going out on the road with a band that is never fewer than eight musicians, with horns and a dedicated backing vocalist on every gig, even radio promos and videos for music magazines.

"It's the kind of line-up Marvin Gaye or Otis Redding had and it seems natural to me," says Nutini, without a trace of arrogance. That is the sort of sound he wants his stage show to make, so these are the forces required.

"Some people say that this is the sound my voice has been crying out for since they first heard me, but some people tell me they prefer it stripped back, just voice and guitar. I say, give it a chance. That's why we put Iron Sky [a pivotal track on Caustic Love, in that crucial track one, side two slot if it was a vinyl album] up on the internet. And I want to fight for the other tracks too. A new perspective is good."

There is every bit as much variation on the new album as there was on the gloriously eclectic Sunny Side Up, but the soul and (old school) rhythm and blues sound of the live set is more of a piece. Nutini worries that he asking a lot of the audience.

"I have been told I should speak more clearly on stage," he tells the cosmopolitan Berlin crowd during the introduction to another new song, Better Man, although they seem to have no difficulty following him. The truth is that, now a more mature frontman, Nutini is not only doing so, he is facing the front almost all of the time and has an enhanced repertoire of showman-like moves.

"It is hard to ask the audience to absorb all those new songs, and the narrative of some of them can get lost," he tells me when we speak again after the short run of European dates. "But the gigs were all good, and especially the Amsterdam one. That was a great audience that really moved with us to a crescendo."

That is the challenge for the Glasgow Barrowland audience next weekend then, but after that, the Usher Hall in May and T in the Park in July, Nutini has his sights on the city's newest venue.

"Once we get to doing bigger shows, it would be good to put together a nice bill with Chvrches and others, take it up a level. I'm hearing that the sound at The Hydro is very good. The SECC would have swallowed me up whole and spat me out, but maybe, God willing, and if the audience is there, this is a time to go for it. Maybe add more visuals. The bigger the stage, the more scope you have for building something."

In fact it is the quality of the new stuff he has written, the force of Nutini's personality and the musical accomplishment of the band that is keeping audiences on side. Beyond the new material, which makes up 80% of the set, the more familiar songs are mostly served up in radical new arrangements, with Pencil Full Of Lead forsaking Cotton Club jazz for industrial Akron, Ohio of Devo at the Boston Arms and Sunny Side Up's ska opener 10/10 reborn as a moody R'n'B ballad. "I never liked the reggae version," guitarist Dave Nelson tells me after the Berlin show. "These guys can play anything - except maybe reggae," Nutini opines of his band when we spoke this week.

That boast was about to be put to the test. The latest phase of the promotional round was a session for Zane Lowe on BBC Radio 1 earlier this week and the selection of an appropriate cover version to play was exercising the singer's mind, with The Beatles' Don't Let Me Down and Buzzcocks' Everybody's Happy Nowadays in contention. He decided on the former but, in Nutini-world, you can bet the options remained open as the clock ticked towards showtime.