"You mention Talk Talk and people either go 'What, that 80s pop group?' or they freak out and say, 'Those are some of my favourite ever records!'" Joan Wasser, AKA Joan as Police Woman, pauses. "They are a really confusing band."

Confusing, mysterious, beautiful and – at least until recently – largely overlooked, Talk Talk's journey from early 80s synth-pop to late 80s post-rock has resulted in a diffuse and tangled legacy. Tracing the line from perky hit singles such as Today, Talk Talk, It's My Life and Life's What You Make It to their final albums, 1988's Spirit of Eden and 1991's Laughing Stock, is to discover that a clearly defined path has gradually disappeared into a thicket of brambles and honeysuckle.

It's taken two decades, but their music has started permeating the wider culture. Wasser is one of 30 artists contributing to Spirit of Talk Talk, a tribute album curated by ex-Depeche Mode keyboard player Alan Wilder and designer, entrepreneur – and rabid fan – Toby Benjamin. Contributing artists range from Linton Kwesi Johnson to King Creosote, White Lies to Peter Broderick, while the musical settings encompass dubstep, folk, industrial, electronica and jazz.

Although each stage of the band's evolution is represented – "We wanted to show that through subtle and sensitive arrangement the entire catalogue justifies serious re-evaluation," Wilder says – the main focus falls on 1986's rootsy but relatively accessible The Colour of Spring album and their final two records. "What was so unusual about Talk Talk is that they experienced a career in reverse," says Wilder. "There was a direct correlation between the quality increase and the popularity decrease. I hope this album can reignite an appreciation of the influence of those last two records."

Spirit of Eden and Laughing Stock are shrouded in mystery, partly because that's the way they are built, but also because the people who made the records are reluctant to discuss them. Talk Talk's singer and creative mastermind Mark Hollis hasn't released any music since 1998 and doesn't interact with the media, while his co-writer and producer Tim Friese-Greene politely but firmly declined an interview on the grounds that "I don't talk Talk Talk talk any more. It was such a long time ago." Former band members Lee Harris and Paul Webb also observe a dutiful vow of silence these days.

Phill Brown is a little more forthcoming. Brown engineered Spirit of Eden and recalls an "endlessly blacked-out studio, an oil projector in the control room, strobe lighting and five 24-track tape-machines synced together. Twelve hours a day in the dark listening to the same six songs for eight months became pretty intense. There was very little communication with musicians who came in to play. They were led to a studio in darkness and a track would be played down the headphones." Asked whether Hollis is an awkward genius or a regular Joe, Brown replies: "All of the above! Stubborn, focused, but humorous. In some ways a genius, but it was a team effort – and it was a big, talented team."

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The resulting album featured six improvised pieces full of space and unhurried rhythm, stitching pastoral jazz, contemporary classical, folk, prog rock and loose blues into a single, doggedly uncommercial musical tapestry. The record label, naturally, had a seizure. EMI's director of repertoire, Nigel Reeve, is now the main point of contact for all things Hollis. Back in 1988 he was in a relatively junior position at the label when Spirit of Eden landed. "There was real nervousness and misunderstanding about that record," he says. "Nobody got it. There wasn't a hit single and they didn't know how to sell it. It caused problems."

The band subsequently left EMI to make the equally uncompromising Laughing Stock for Polydor. Both albums sold poorly and were largely overlooked at the time of their release. Slowly, however, they found their constituency. Many of the artists on Spirit of Talk Talk vividly recall being turned on to these records by fellow musicians. For Wasser it was Antony Hegarty's violinist Maxim Moston; Peter Broderick remembers "a couple of the Efterklang guys sitting me down in 2007, playing me Spirit of Eden and telling me how much of an influence it had been"; Lone Wolf's Paul Marshall acted on a tip-off from Wild Beasts. "I could not believe I'd missed these albums. They shot to the top of my list of all-time favourite records."

Just what is it that makes this music so compelling? "It's uncompromising," says Guillemots' Fyfe Dangerfield, who covers The Rainbow, in collaboration with Thomas Feiner and Robbie Wilson. "In one way it's slow and quite laid-back, but there's this uncomfortable, abrasive quality. They were doing such poppy stuff before, but this was obviously what was inside Mark Hollis's heart, and it feels like it. There's no notion of the outside world at all."

Like a puzzle no one really wants to solve, late period Talk Talk stubbornly refuses to give up its secrets and is therefore endlessly open to interpretation. For Dangerfield, the music feels quintessentially English. For Wasser, who covers Myrrhman, "it has a blues thing that makes me think of New Orleans. Like a big, old house full of ghosts and swirling memories. The spectrey vibe." Then there's Hollis's voice: unsettling, intense, not pretty but oddly beautiful. "There's an effortlessly devastating and passionate tone to it," says White Lies' Charles Cave. "It sounds like he's always struggling, and I love to hear that."

Covering these distinctive, amorphous songs throws up a series of challenges to any musician. "You almost need to take the atmosphere as being as much part of the track as the melody and lyrics," says Dangerfield. "In the end it became about interpreting the feel of it." King Creosote, who turns Give It Up into a sprightly squeezebox number, wanted "to pick a song that I could somehow make ring true. It's not my favourite. I wouldn't go near my favourite Talk Talk songs with a bargepole!" Toby Benjamin mutters wryly that some fans will regard the whole idea of a covers album as "sacrilege".

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The band's impact on modern music is palpable but hard to quantify. Reeve acknowledges the irony that, not long after Talk Talk were kicked off EMI for delivering Spirit of Eden: "Radiohead produced a similar kind of record and nobody batted an eyelid." Elbow are huge fans, while members of Arcade Fire and Bon Iver appear on the tribute album. "Judging by the feedback and the general level of interest from everyone who wanted to be involved, their influence is massive," says Wilder, who suggests artists are drawn not so much to a sound as a sensibility. "The meticulous and sheer bloody-minded, anti-establishment approach speaks to musicians who care passionately about their craft but find themselves diverted from their vision by outside influences."

Hollis's distaste for image-building and promotion worked against the band at the time; now it's become an advantage, feeding into the perfect myth of an artist who achieved all he wanted and then walked away. Although Hollis chose to play no part in the project – "We got feedback from a friend saying he wished us luck and that he liked the Matthias Vogt Trio's version of April 5th, but that's it" – Wilder says that his guiding criteria when listening to each cover was "to try and place myself in the head of Mark Hollis and imagine if he would enjoy what he heard". According to Reeve, however, "I'm not sure Mark will ever get around to listening to it. We've played Talk Talk stuff in the office when he's been there and he won't listen to more than 30 seconds before he wants it turned off." Last month, however, news emerged of his first music for 14 years, which will feature on the US TV drama Boss on 21 September (though not on the stream of its soundtrack).

Having sued EMI following the unauthorised release of the 1991 remix album History Revisited, relations between Hollis and the label are now cordial. He and Reeve have been collaborating on the tracklisting for a new Talk Talk compilation, Natural Order, due later this year. "Mark pops into the office every few months," he says. "We have a coffee and a chat, mostly about football. He's a bit of a Spurs fan." The mythology surrounding his retreat into silence apparently bears little relation to the day-to-day reality. "He lives a very normal life, it's just like he changed jobs," says Reeve. "There's nothing in Mark driving him to make a new record, I don't think. In all the conversations I have with him he says: 'I did it. Full stop.' He got to where he wanted to go." Finally, the rest of the world is catching up.

• Spirit of Talk Talk is out now on Fierce Panda. An accompanying book is published in September by Rocket 88. Details: spiritoftalktalk.com