"That's why we're back on tour today," Kemp says. "You can't have a band that lasts that long and is that successful just based on the way you look or if you can put a poster up on a girl's bedroom wall or any of that - it's about the songs. And that's what Spandau was about."
Yes, the group behind such stone-cold cheese-pop classics as Gold and True are back and, having re-formed only last year after splitting up in 1990, they're making up for lost time with a crowd-pleasing show.
"Usually when you go out on tour you do kinda six or seven songs from your new album and then you kinda do a few hits from the different old albums," Kemp says. "This time it's complete wall-to-wall hit records. I think that's why everybody in the audience is having so much fun with it."
Kemp sounds relieved to report that the band is having fun too, which is pretty impressive when you consider that for much of the 1990s and '00s, the only time singer Tony Hadley, drummer John Keeble and multi-instrumentalist Steve Norman saw him and his guitarist brother Gary was in court because of a stoush over songwriting royalties.
"It was traumatic for everybody," Martin Kemp says. "But I remember the first gig that we did in Dublin when we got back on the road: just before that curtain dropped and the band were back on stage was the most incredible feeling that we'd all got that far, because for 20 years, y'know, no one spoke to each other.
"To actually stand on stage with those guys that I've known since I was 13 and start touring again was unbelievable."
The question was whether they would be able to reclaim the popularity they enjoyed in the '80s.
"It was a funny old thing," he says. "Back in October, when we first put the shows on, we really didn't know how it was gonna go. The band was, like, super successful in the '80s but we hadn't done anything for 20 years, so it was kind of like, just put your toe in the water and see what happens.
"When a band usually puts a show on, they can judge how many tickets they're gonna sell because of what number you are in the charts or how many records you're selling but we didn't have any of that. So it was kind of, put one show on, put another on ... and in the end it was the biggest tour that we've ever done in Britain."
One of the more endearing qualities of Spandau Ballet - just look at their old video clips for proof - was the band's apparently healthy sense of their own ridiculousness. The observation makes Kemp chuckle.
"But at the time we didn't think it was ridiculous," he says. "We thought it was for real!"
Even when they moved from the vanguard of the new romantic underground (early Spandau singles Chant No. 1 and To Cut a Long Story Short still sound cool) to the upper reaches of charts worldwide with the likes of True?
"Well, the only bands that ever survive are bands that evolve. If you start out as a cool band and you're only playing to kind of these small clubs, is that what you wanna do forever?" says Kemp. "Every band wants to be the biggest band in the world and you have to kind of choose your route to get there. In the end we turned out to be one of the biggest bands of the 1980s.
"Y'know, most bands have success over three or four years. Spandau had a complete decade of it."
Spandau Ballet play at Rod Laver Arena on April 21. Fellow 1980s stars Tears for Fears are the support act.