In the context of a history of the early goth scene, having a section about Metal is about as relevant as having a section about Mod or Ska. All three scenes were around (in a revived form) at roughly the same time as the early goth scene, but they had very little interaction with or influence upon it.
However, an awful lot of people seem confused on this point, so maybe I'd better explain.
The late 70s and early 80s were very different to what came later - even just a few years later, when goth took on rock influences and rock became fashionable again.
At the end of the 70s and start of the 80s heavy metal, as one of the many things punk had been reacting against, was deeply unfashionable. Goth came from punk roots (with influences from Bowie and co as described elsewhere) and largely inherited this deep-rooted contempt of all things "metal". Metal was regarded as archaic and a thing of the past, whereas most early goth bands saw themselves doing something new, fresh and in some cases experimental.
Later on, metal was to absorb influences from goth, punk, industrial and even rap, but at the time the most that could be said of it was that the impact of the punk revolution had resulted in a somewhat harder sound (later on, punk influences on the likes of Metallica would completely change metal, but that's a different story).
Certainly in the early 80s the two scenes were poles apart, in both music and fashion - goth was darkly glamorous, with an androgynous look, lots of makeup and fishnets, whereas the metal scene was still largely biker chic, with denim and patches. Essentially, goth had a feminine edge whereas metal was still very masculine.
As for rock influences, I can only think of two early bands who were overtly influenced - Play Dead (Black Sabbath) and The Sisters of Mercy (Rolling Stones, Led Zeppelin). Neither were major players in the early scene, though the Sisters were later to be partially responsible for the shift to Goth Rock. It should also be stressed that those rock influences were simply one of many, for both groups (the Sisters were just as much influenced by, say, Leonard Cohen), and that neither group had contact with the contemporary metal scene.
I should also stress that Black Sabbath, whilst having been responsible for an awful lot of things, were not in any way responsible for the early goth scene.