The Goth movement really began as the darker side of some more mainstream, but equally flamboyant musical reactions to the death of the Punk movement in the UK. Adding to a vibrant and diverse music scene which included the famous New Romantic scene but also NWOBHM (New Wave of Brtish Heavy Metal), Ska, Futurist and others.
The bands that shaped the early scene are not generally the ones that people will think of as being stereotypical Goth, instead being bands like Bauhaus, UK Decay and the Virgin Prunes, and of course clubs like the Batcave.
I will not pretend to know more or be able to do better than those who have written (quite extensively in Mick Mercer's case) on the subject of early Goth, so instead I bow to their work and include several links which I found provided a good grounding on the subject.
Pete Murphy - Bauhaus
http://www.scathe.demon.co.uk/histgoth.htm - History of Goth - great website that details a lot of the early stuff!
http://www.mickmercer.com/gothhistory1.html - This is Mick Mercer's website. He is the author of The Hex Files, Gothic Rock and the Gothic Rock Black Book all of which contained large passages on the erarly goth bands and clubs. It is to his writing I first turned when becoming interested in Goth, aged 17. His publications these days mostly are released online, and his LJ mickmercer contains almost daily reviews.
http://www.religioustolerance.org/goth.htm - Not a Goth history website, but one I stumbled across while doing some research. It's a religious website, which tried in the aftermath of Columbine to give a tolerant overview of what a Goth is. I think they did a reasonably good job.