A week after joking at a party that he was in a band, Rudy Tambala found himself at the start of a journey that produced some of the 80s' most extraordinary music

The way Rudy Tambala tells it, his band AR Kane should never really have existed. Surely it was a dream? Two young dreads from east London, friends since they were eight, who both – independently – stumbled across the Cocteau Twins on Channel 4 music show The Tube in the mid-80s … and found their lives were suddenly changed.

"They had no drummer," laughs Tambala, now a "digital music strategist". "They used tapes and technology and Liz Fraser looked completely otherworldly with those big eyes. And the noise coming out of Robin's guitar! That was the 'Fuck! We could do that! We could express ourselves like that!' moment."

The music Tambala and his partner Alex Ayuli made in a burst of intense creativity between 1986 and 1994 – some of it now collected on a new compilation, The Complete Singles Collection – still sounds utterly free-floating, like they pulled it out of the ether. It would also change British pop in various ways, encouraging other groups to experiment with feedback and twist indie rock into new shapes, and forming a crucial if largely accidental part in UK house music's commercial breakthrough.

They'd grown up going to "really, really weird clubs", from new romantic hangouts to early electronica parties. Alex was part of a dub soundsystem, while Rudy came from the jazz funk scene, "a mix of gay and straight, black and white and Asian". The music they made as AR Kane – blending dub, feedback, psychedelic dream-pop, house and free jazz – can still be heard in artists such as Radiohead, Four Tet, Animal Collective and Burial.

"And My Bloody Valentine," Tambala says. "They were a jangly indie band until we put out Baby Milk Snatcher [in 1988]. Suddenly they slowed it all down and layered it with feedback. And they did it better than us, which was interesting."

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A few days after seeing the Cocteaus on TV, Tambala met a woman at a party who knew Ayuli and asked how they knew each other. Jokingly, Rudy said they were in a band together. He explained how they'd played around with Citizen Kane and The Mark of Cain and arrived at AR Kane, thinking it was "really, really funny". So when the woman asked, "What's the band like?" Tambala riffed away, saying: "It's a bit Velvet Underground, a bit Cocteau Twins, a bit Miles Davis, a bit Joni Mitchell."

"I was stoned, probably," Tambala laughs. A week later, a producer who worked with the One Little Indian label called and told them to send in a demo because the label was interested in signing them. Except, of course, the band barely existed.

"We had no tracks," Tambala says. "No songs. Only a bit of equipment and a lot of ideas."

The pair immediately began to record using two cassette players, bouncing tracks between them. It couldn't have been any more lo-fi, but soon they had enough for a demo. One Little Indian's founder, Derek Birkett – a former member of the confrontational anarchist punk band Flux of Pink Indians – loved the tape and wanted to see them play live. In a fevered panic, the pair hired Tambala's sister Maggie to sing backing vocals, they put a mate on drums, another on bass ("he could only play one note") and invited Birkett and his "hardcore skinhead, punk, anarcho-type" gang to their Docklands rehearsal space.

"They were scary people," Rudy says. "We were kind of young and pretty and we made this absolutely disgusting noise. Straight after we played, Derek went: 'You're shit. Let's make a record.' We'd been a band for about two weeks."

When the time came to sign their one-off single deal AR Kane went to Birkett's house in south London where he had punks living in teepees in the garden. Birkett took them up to his bedroom ("a fucking shithole") and told them: "I've got two bands and one of you is going to be really successful." He then pulled out a picture of what appeared to be a six-year-old girl holding a frog. "And that was the first time I saw Björk," Tambala says.

A string of tumultuous, riotous gigs followed as AR Kane promoted their When You're Sad EP to crowds who simply didn't know what was going on. "They'd see these dreads get up on stage and expected us to play reggae," Tambala says. "When they got a wall of feedback, they figured there was a technical problem, and they would leave, but that was the set."

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Eager to record more songs, the band sent a tape of a new track called Lollita to the Cocteau Twins' label, 4AD, which offered them a deal. "But they were all weird, too," Tambala says. "Vaughan Oliver [4AD's inhouse designer] went round and shaved everyone's heads every week, even the women. They were all wearing black with shaved heads and at first we thought: 'Wow, these guys are really esoteric and out there!' But we ended up thinking, 'What the fuck is going on?' They looked Zen, but they weren't."

While at 4AD, AR Kane would help create one of the great records of the early acid house era – and the first sample-based UK No 1. Pump Up the Volume was one half of a double A-side single released in 1987, which pitched AR Kane's squalling guitars over an array of samples and a thumping house beat. Everyone expected the single to do well, perhaps shift 100,000 copies. When it sold by the million it nearly finished 4AD, which simply couldn't deal with a record that big.

"It blew the label apart," Tambala says. "It destroyed a lot of illusions."

Creatively, AR Kane's high-water mark came with their 1988 debut LP, 69, a brilliantly sprawling and ambitious collection that was immersive and playful – and completely off the wall.

"69 is a gem," smiles Tambala. "We wanted to go as far out as we could, and in doing so we discovered the point where it stops being music."

Two more albums followed, but, as Tambala says, "the energy had gone" and the pair went their separate ways in 1994. "Ultimately, whether you're lovers or musicians or artists or a political party, if you haven't got that kind of connection where you completely get each other on a telepathic level, then you're in trouble," Tambala says. "For a while there Alex and me had that. We were really good. Just listen to those tracks, we piled so many ideas into every fucking song!"

• The Complete Singles Collection is out on 1 October on One Little Indian. You can buy it here.