Edinburgh's Young Fathers, alongside Chvrches probably the hippest new band to have emerged in Scotland in recent years, and boasting the Scottish Album of the Year (SAY) Award and 2014 Mercury Prize accolades to prove it, did not arrive quite as singularly as it may seem. The often little-remarked Scottish hip-hop scene has other successful names including Stanley Odd, Hector Bizerk, Loki and MC Soom T, all of them as distinct and as far from the indie and folk-rock mainstream.

Keep trawling back through the annals of pop north of the border, tracing that lineage, and you will eventually encounter the legend that is Boots for Dancing, the punk-funk combo that began life in the capital as a post-pub piece of bravado and rolled through no more that three years of existence with a constantly changing line-up around frontman, vocalist, proto-rapper and mean mover Dave Carson. They left a recorded legacy of just three singles and a trio of sessions for the John Peel radio show. The legendary DJ's crucial support hardly sets Boots for Dancing apart from many other bands in what is now termed the post-punk era of 1979 to 1982, but his assertion that they were one of the few bands whose music was liable to persuade him on to the dancefloor is worth noting.

Now, some decades later, there is a Boots for Dancing album, newly released on the Athens of the North label run by Euan Fryer and the culmination of three years work by Fryer and Carson. Entitled The Undisco Kidds - a title that pays studied homage to the sound of George Clinton's seminal American band Funkadelic who inspired the less musically literate Edinburgh teenagers back in the day - the 14-track disc includes the entirety of two of those Peel sessions and one song from the third, together with four tracks recorded in 1981 at Tony Pilley's equally legendary Barclay Towers studios in Edinburgh. That visit to the studio produced the band's third, self-released, single, Ooh Bop Sh'Bam, but it is the only song on the whole project that has previously been commercially available, which makes the album much more than an exercise in vault-raiding nostalgia.

Particularly curious at first sight is the omission of both the previous singles, released on Bob Last's Pop:Aural label, The Rain Song, and the twelve-inch floor-filling anthem that kick-started the whole story, the song Boots for Dancing itself. As Carson explains, there are both musical and legal reasons for their absence.

"The work in putting together a Boots album - and it was Euan driving it - was in tracking down high quality recordings. The sound on the Pop:Aural recordings was much more compressed and not at all like the rest of the music we could find. And there is still some questions about the status of them in terms of what we signed at the time.

"It was simpler to licence the Peel sessions from the BBC and we were lucky to track down Tony Pilley. We wanted to make it sound like an album as an entity rather than the product of different sessions. The recordings were made over two years but they are not too disparate. I am totally amazed by it."

"It is not about revisiting the past and past relationships, but about finding something and putting it out for people to enjoy."

In that endeavour, Carson found the perfect partner in Fryer's Athens of the North operation, whose main business previously has been tracking down rare soul and disco 45s and reissuing them in high quality - and not inexpensive - seven inch pressings. Naturally, although the first release of The Undisco Kidds is on CD, there will be a vinyl version.

The story that Boots for Dancing is part of is one of a very vibrant Edinburgh scene, which is very fondly recalled by those who were there. Its alumni included Jo Callis, the guitarist and songwriter who passed influentially through the ranks of Boots on his journey between the Rezillos and The Human League. The manager of Boots for Dancing, and later the equally before-the-wave So You Think You're A Cowboy?, Alan "Pinhead" Proudfoot, would occasionally employ this writer to drive his bands to and from gigs. It is an era that is beautifully evoked, and meticulously recorded, by The Herald's Neil Cooper in a lengthy essay in the new disc's booklet.

"The coherence in the story is all Neil's," says Carson. "He interviewed me for two-and-a-half hours and then sent me a first draft with all the cross-references he had found through drawing me out and triggering my memory. He really opens up the story. There was no such thing as post-punk back then - that was invented in retrospect - but it was a development of the ideas of 1976 and 77 in that we were all about challenging things."

The Boots for Dancing album has - eventually and coincidentally - arrived at a time when the story of Scottish music-making of the period, particularly in Edinburgh as well as better-documented Postcard-label Glasgow, is being rediscovered, due in no small part to Grant McPhee's acclaimed documentary film Big Gold Dream. Gideon Coe airing an old Boots for Dancing Peel session on BBC Radio 6Music also gave Carson and Fryer's efforts "a bit of a boost", as Carson puts it.

What is clear is that The Undisco Kidds is an album that Boots never stood still long enough to make at the time. The variety in the music is terrific, ranging from the foot-stomping chants of Get Up and Ooh Bop Sh'Bam that grew straight from that eponymous punk-disco debut, to the lounge supper club jazz aesthetic of Style in Full Swing and South Pacific and culminating in the uncategorisable Bend and Elbow, Lend an Ear. While the skill of the young musicians develops in provocative directions, the common thread is Carson's way with an ear-catching lyric, cheerfully plundering a hinterland of showtunes, gospel and r'n'b for memorable phrases to repurpose.

"My main regret is that we didn't get into the studio more," says Carson, "because the other great instrument is the mixing desk. Most of these tracks were recorded with very few overdubs, and I'm very happy that people can now understand the range and variation Boots were capable of."

The Undisco Kidds by Boots for Dancing is out now on Athens of the North