Throughout the 1980s there was a movement towards a more politicised music scene, lead by groups like The Levellers and, most notiably to my mind, The Men They Couldn't Hang. This group, with members sporting names like Swill, Cush and Jon (!) produced three albums between 1985 and 1987 (Night of a Thousand Candles, How Green is the Valley, Waiting for Bonaparte) which plugged into the ziestgiest of the age, as well as bringing some fantastic music to the world. Of these to my mind the best is the middle album, How Green is the Valley, which includes my all-time favourite political song, 'Ghosts of Cable Street'. This song is a song of praise to the brave working class - Jews and Gentiles, who stood up to Moseleys fascist blackshirts in a small East London Street in 1936.
Other songs on this outstand album sum up the fear of living on an oilrig - Gold Rush - a clash of working class political beliefs - Shirt of Blue, and simply being alive and enjoying life - Dancing on the Pier. Now, obviously others may listen to these songs and get something totally different from then, but that is the joy of any classic album, the fact that one listener can get something totally different from the songs whilst the next gets something different altogether!
If you want to know what the 1980s were all about musically away from the chart stuff of the era then this is a great starting place. You will not hear Wham, or the New Romantics, or Disco here, but you will hear an authentic slice of '80s music that says as much about that era as any other group I can think of.