For more than four decades, the songwriting duo of Chris Difford and Glenn Tilbrook have penned indelible pop songs that distill huge stories down to their essence, then add a few zinging hooks, memorable guitar licks, and the high-low vocal interplay of Tilbrook and Difford for good measure. Tracks like the rueful “Tempted’’ and the galloping “Another Nail in My Heart’’ combined impeccable songcraft with pure pop pleasure, and still exist on their own plane.

After splitting in 1999, the band reformed in 2007 for live shows that ran through their storied catalog. But it wasn’t until 2015 that they released their first Squeeze recording in 18 years, the sterling ’70s throwback “Cradle to the Grave.’’ While new songs like the sun-dappled “Happy Days’’ and the dryly observational “Only 15’’ possess the radio-ready melodies and keen character detail that define Squeeze’s greatest works, the process that led to their existence was a bit different.

“It used to be more individually proportioned — I would write the lyrics, and Glenn would write the music,’’ says Difford. “Never the twain shall meet, and the songs would come together. That’s how life was — our communication wasn’t great, but that’s the way we worked. On this record, we have had the fortitude of spending time apart, and we learned a bit more about each other, and about how to write songs. The collaboration was a lot closer than it used to be. It’s been an interesting departure.’’

“Cradle to the Grave’’ was written as a companion to a BBC sitcom of the same name; set in the ’70s, it follows a 15-year-old south Londoner and his family. Getting back into the mindset of that decade, which also saw the formation of Squeeze, was, for Difford, a pleasure.

“The ’70s were a place that I love very much,’’ he says. “I feel like it was my 1960s — I had a great time, the music was brilliant, the 1980s were closing in, and it was just terrific. To go back there was just wonderful. It’s a place that I visit a lot in my head, musically, spiritually. It’s just a great place.’’

After the band gigged around London for a few years, Squeeze’s first album, produced by the Velvet Underground’s John Cale, came out in 1978. (The band’s name is a tongue-in-cheek homage to the VU’s most derided album; the deluxe edition of “Grave’’ features a stretched-out cover of the Lou Reed track “Hangin’ ’Round.’’) Their initial burst of singles — including the grandiose “Take Me I’m Yours,’’ the devastating “Up the Junction,’’ and the conflicted “If I Didn’t Love You“ — helped define a thread of new wave that placed songcraft and storytelling front and center. (Difford notes that he and Tilbrook are looking to eventually stage a musical focused on the band’s songs, although “to satisfy us, we need to find the right book.’’)

“Cradle’’ only strengthens Difford and Tilbrook’s status as one of pop songwriting’s all-time premier duos, with the pleasures offered by songs like the disco-tinged “Nirvana’’ and the sparkling “Honeytrap’’ drawing extra oomph from taut structures and lacerating wordplay.

“Sometimes songs really need to be looked at and shaken about before they have the Quality Seal put on them. Glenn’s very good at that; I’m a little less worried about quality, I don’t know why,’’ Difford says, laughing. “I just like to get things done, and go with the feeling. But what’s absolutely brilliant is to have Glenn by your side, because he can cut straight through that.’’

Monday night’s sold-out show at The Wilbur will have songs from “Cradle’’ and Squeeze’s storied back catalog. “When we play the old songs, because of the structure of most of the songs, they remain the same, [although] the excitement is different each night,’’ says Difford. “I mean, there’s not much you can do with ‘Pulling Mussels From a Shell’ — it is what it is, and it’s a wonderful song, but you can’t change the arrangement. It’s not like the Grateful Dead, where you can just go and start jamming in the middle. It’d be wonderful if it was, but it isn’t going to happen.’’

But that precision is not only part of Difford and Tilbrook’s charm, it’s what helps their work stand the test of time.

“Right now it almost seems like they’re practitioners of a kind of pop that isn’t made much anymore — the real craftsmanlike work in both the melody and the lyric, the attention to detail,’’ says Stephen Thomas Erlewine, senior editor of pop at TiVo. “You just don’t see that in a lot of bands anymore, and you wind up appreciating how finely wrought their songs are.’’

Maura Johnston can be reached at maura@maura.com.