"We've got three or four photos. Can you imagine if it were now? It would be selfies like crazy," says Woodward. "But they were on an old Instamatic, so they're not that clear."
There have been many iterations of Bananarama since that time: the Stock Aitken Waterman years, which led to band member Siobhan Fahey quitting in search of an edgier musical direction; a period with Fahey's replacement, Jacquie O'Sullivan, which never felt quite right; and for the past 28 years Dallin and Woodward have operated as a duo. When Fahey rejoined in 2017 for a one-off tour it became quite an event, and the renewed interest prompted them to release their first album in a decade.
In Stereo is a collection of exuberant pop that recalls the sound of their heyday.
"It's really odd, but whatever we do and whatever style we might tackle, we always sound like us," Woodward says.
More than anything, they sound like two friends having a ball.
Classic Pop magazine described one of their recent gigs as having the air of "a massive hen night piss-up", and meant it in a good way. They're not remotely offended.
"I think we've got the tracks that everyone wants to sing along to. A lot of people say, 'God, I've forgotten you've had so many hits!'"
The pair have an "unbreakable" bond, forged during their schooldays in Bristol. Sitting alongside one another in a restaurant near Dallin's home, they laugh a lot, finish each other's sentences and hold the same opinions on pretty much everything, not least the fact that they deserve a bit more credit.
Bananarama were famous around the world, topping the US chart with Venus. Yet it was Duran Duran, Spandau Ballet and the like who were regarded as the era's success stories.
"Women just weren't taken seriously," says Dallin. "I remember the Brit Awards in the 90s did a look back on all the 80s groups and we didn't get a mention.
"Every bloke under the sun had a mention," Woodward mutters.
"It made me very angry at the time," continues Dallin. "You think, where's our recognition? We're not asking for awards or anything, but just recognise what women do."
It is remarkable to look at a picture of the crowded Band-Aid line-up and realise that Bananarama were the only women other than American singer Jody Watley. But as Woodward points out, that's how the music industry was. "Most of the people we worked with were men. And the women were secretaries."
The band launched themselves on the music scene through a combination of blagging ability and sociability. They had moved to London and lived in the YWCA when they made friends with Paul Cook, the Sex Pistols drummer, who invited them to move into his band's rehearsal room.
They made up their own dance routines, chose their own clothes and giggled their way through Top of the Pops appearances although "we grew in confidence as we went along".
I wonder what they think about bands like Little Mix, who always seem to be performing in their underpants. "Pants are very popular, aren't they?" deadpans Dallin.
"I'm actually quite proud of the fact that we made a success of ourselves in a donkey jacket and DMs, without any thought to sexualising what we were doing. I don't know if there's pressure now on girls to perform like that or whether that's what they want to wear — if that's what they want, there's nothing wrong with it," says Woodward, who has a son, Tom, 32.
Without Bananarama, would Little Mix exist? Certainly the Spice Girls acknowledge them as an influence. The reunion tour with Fahey (who enjoyed success as one half of Shakespears Sister after Bananarama) served as a reminder of how much fun they were. It also ended a lengthy rift between the trio. What is Fahey up to now? "Don't know," they say in unison, and the conversation swiftly moves on.
"But we have other friends, you know. We're not joined at the hip!" Dallin, who has a 27-year-old daughter, Alice, lives in north London, while Woodward is based in Cornwall (she split from Wham!'s Andrew Ridgeley in 2016 after 25 years together).
Their new album is self-funded, and they're quite open about the reasons. "Our career is 36 years old, so there weren't loads of people dying to sign us, which I think is the case with most bands of our era."
Woodward has just turned 58 and Dallin is 57, though they look a decade younger and understatedly glamorous. Dallin adds: "They might say, 'You're in your 50s, why are you making music?' Why wouldn't I? It's all I've ever done."