The first encounter between comedian Julian Clary and singer-songwriter Barb Jungr did not go well. It was 1985 and Julian admits he was in typical tease-the-punter mode as he worked the audience at the Bush Fires cabaret club in Shepherd’s Bush, London. He approached Barb, who was wearing a bandana, and inquired if her head was hurting her, much to everyone’s amusement.

“It was a very chic orange-and-white bandana,” Barb huffs in mock outrage. She had been waiting to go on after Julian, and sat in the audience to watch, as performers on the same bill often do. Having started out in a new-wave gospel band called the Three Courgettes, Barb and guitarist Michael Parker were performing as the alternative cabaret duo Jungr and Parker, while Julian was doing standup as the Joan Collins Fan Club with whippet crossbreed, Fanny.

Backstage later that night, they clicked instantly after Julian apologised, saying he would never have cracked that joke had he known Barb was also a performer. Keen to expand his act with music, he and Barb started writing comedy songs together, such as Mincing Machine. The following year, the pair shared a cramped flat at the Edinburgh fringe and “had as much fun as it’s possible to have in three weeks”, recalls Julian, who then joined Jungr and Parker for several tours.

Julian’s big TV breakthrough came in 1989 with Channel 4’s camp gameshow Sticky Moments With Julian Clary, with Jungr and Parker providing the music for his closing number. Their collaborations continued until Barb’s eclectic composing and performing career for stage and film began to take her around the world. Nevertheless, the 39-year friendship has endured. Although Julian is now based in London and Barb in West Sussex, they speak regularly on the phone and meet up for supper several times a year. They agree that their easy rapport makes them feel as if their friendship was meant to be.

They have also successfully surfed their differences (“I’m languid, she’s driven,” says Julian). “Julian will be singing I Love a Knob, while I’m wondering whether to have a go at [Bob Dylan’s] Desolation Row,” says Barb. “But I’ve never found Julian’s show too rude,” she adds.

Their bond has even survived Julian bossing Barb into a glamorous makeover with “proper” stage clothes, mascara and lipstick (“You’re a singer: the focus is on your mouth”). “But I’ve always been a wild-in-the-wind, out-on-the-moor kind of person – and I can’t wear lipstick if I’m playing the harmonica,” says Barb. “So cut the harmonica,” Julian shoots back.

In turn, he has learned to overlook his loathing of Bob Dylan and Leonard Cohen and love Barb’s reinterpretations of their songs, sung in a jazz style that has drawn comparisons to Nina Simone and Peggy Lee. “I like songs that make you smile, which doesn’t apply to Dylan and Cohen. But I’m a big fan of Barb’s singing – it’s transporting. She always delivers and I don’t want it to stop,” he says.

They have always got on with each other’s spouses – Julian’s husband, Ian Mackley, and Barb’s late ex-husband, Dan Bowling. “I’ve seen people come and go over the years and I was very happy when Julian married Ian,” says Barb.

“We’ve been through a lot – amazing times and sad times. We know each other very well, so we support each other,” says Julian, who wrote in his autobiography A Young Man’s Passage about the death of his boyfriend Christopher from Aids in 1991. In what Julian called a “beautiful” tribute, Barb wrote a song about Christopher that Julian says he still plays when he’s thinking about him.

Likewise, Barb says: “If I’ve got a problem, I will ring Julian. I had 10 years of bereavement when everybody I knew seemed to die, including my two sisters. Julian and I are both very family-oriented, and I knew I could just turn up at his place and burst into tears because he’s such an extremely kind person.”

The pair share a fantasy of living together in a “great big seaside house called Showbusiness Lodge”, but, meanwhile, make do with the phone calls.

According to Barb, “Julian is very funny and cultured. We are both impulsive and follow our hearts and we both have psychic skills: we’ve spent many a night under a full moon.”

“Barb makes me laugh,’ says Julian. “She’s very easy-going and also very straightforward: you’re going to get the truth from her.”

Barb Jungr performs Singing Into My 70s at Crazy Coqs, London W1, until 11 May. Julian Clary is touring with A Fistful of Clary until 14 June.