Squeeze. (Danny Clifford/Courtesy of the Artist)

Pop songs are variously about: falling in love, breaking up and/or getting back together again. That pretty much sums up the ongoing history of Squeeze, the British band that delighted fans with such songs such as “Pulling Mussels (From the Shell),” “Up the Junction” and “Black Coffee in Bed.”

After calling it quits twice, mainstays Glenn Tilbrook and Chris Difford are back together again, bringing Squeeze to Wolf Trap on Thursday, when they open for the B-52s.

Calling from the tour (“I am somewhere in New Jersey. That’s all I know.”), Tilbrook reflected on his nearly 40-year collaboration with Difford. They met in 1973 when the then-15-year-old Tilbrook answered an ad 18-year-old Difford had placed in a London shop window. The ad said a band with a record deal was looking for a guitarist.

There was no record deal. There wasn’t even a band. There was just Difford and his pile of lyrics.

“Chris was the first person I met that wrote songs besides me,” Tilbrook says. “When I met him, I loved the way that he wrote and I think he felt the same about me. … He was much more gifted lyrically than I was and I think my tunes were better than his.”

It proved a winning combination. On early albums such as “Cool for Cats” (1979), “Argybargy” (1980) and “East Side Story” (1981), Squeeze (which at the time included keyboardist Jools Holland, drummer Gilson Lavis and bassists Harry Kakouli and, later, John Bentley) spun tuneful, tightly composed vignettes. The songs brimmed with details of everyday life, Difford’s “kitchen sink lyrics” made sublime by Tilbrook’s sparkling melodies. Often, Difford’s lower voice provided a sandpapery undertone to Tilbrook’s soaring tenor.

The songs have always been unapologetically British, their plots unspooling in pubs and on windy commons. They reference tellies and tenners, borstals and bedsits. “Tempted” – the 1981 hit sung by Squeeze’s then-keyboardist Paul Carrack – begins “I bought a toothbrush, some toothpaste, a flannel for my face.”

Glenn, did anyone ever suggest you should maybe sing “A washcloth for my face” instead? You know, translate for the American market?

“No,” he says with a laugh. “For me when I was growing up and I was listening to Chuck Berry or Bob Dylan or Randy Newman, they were talking about American things I didn’t understand. I think people just fill in the gaps. … I’ve never felt the listener ever had to understand everything to get the big picture. And a little mystery can be charming, as long as it’s not too self-knowing.”

Squeeze’s best songs are about the small picture, pointillist pop that tells heartbreaking stories in three-minute slices. The word that critics once invariably applied to Difford and Tilbrook’s work was “clever.” Did the two ever tire of seeing that slightly damning word?

“I can really only answer that by saying I don’t think of us as being clever writers,” Tilbrook says. “I think that what we do is an attempt to satisfy ourselves. That’s really all you can do. …I remember in early Squeeze thinking ‘People are going to love this.’ I never understood why people didn’t. I find it hard to understand how comparatively simple things people seem to go nuts about.”

When talking with Tilbrook, there’s a wistful sense of what might have been. Squeeze was part of a late 1970s London “new wave” music scene that brought forth such quirky and refreshing artists as Elvis Costello, Nick Lowe and Wreckless Eric, performers who were critically acclaimed but not as commercially successful as, say, the Police.

“We were successful, but if you asked me if I'd rather be Costello or the Police, I know what my answer would be, easily,” Tilbrook says. He means Costello, who co-produced 1981’s “East Side Story.”

“He’s always been looking ahead and he’s never stuck to one thing,” Tilbrook says. “That was Squeeze’s mistake. You can't go back over that but that’s what we did. Elvis didn’t do that. He was smart, so hats off to him. The Police … I know a lot of people like them.”

Squeeze broke up in 1982 and again in 1999, before reforming in 2007, Difford and Tilbrook the only original members. During their various times apart both Difford and Tilbrook engaged in solo careers. Tilbrook formed a new band, the Fluffers. On one of his solo tours, he famously led the crowd at Arlington’s Iota outside and serenaded them in the parking lot.

“Really, it was only going back to solo work and having my band the Fluffers that I really connected with how exciting things could be if you worked at it a bit more,” Tilbrook says. “I thought, I never want to lose that with Squeeze. I’d hate it to become the way that it did become, once upon a time. I don’t think it has. I think it’s still exciting. That’s my opinion.”

For the first time in 12 years a songwriting team that’s been compared to Lennon and McCartney is again writing together.

“We're now embarking on a batch of writing,” Tilbrook says. “To my mind, there’s no point in doing new Squeeze stuff unless it’s going to be the best Squeeze stuff there’s ever been. Setting the bar that high is very hard. So we’re taking time to work on the songs.”

Tilbrook says there’s one song he’s particularly excited about, one they’d been hammering at on and off for three months when “the tune just wrote itself. It’s one of my favorite Squeeze songs ever. You have to pass that point before you can carry on properly.”

And the song’s title?

“‘Tommy,’” Tilbrook says. “No relation to the Who song.”

In their heyday, the Who were headlining festivals and packing stadiums. Tilbrook doesn’t mind that Squeeze isn’t.

“When Squeeze split up I found that, perversely, although my gigs got smaller, my enjoyment of them got bigger,” he says. “I learned something very valuable: I never want to be involved in anything again that I don’t enjoy. … I’d rather play to six people and have a great time – really, honestly I would. I’m in the very privileged position to be able to play to a few more than that with Squeeze, so why don’t we get this right?”