Yes, we know they aren't a Cumbrian band, but their beginnings were very much involved with the area and Carlisle in particular.
Sabbath even had a roadie from Egremont (born in Cleator Moor), David Tangye, who has co-written a book about his days with the band "How Black Was Our Sabbath" (available from HMV, Amazon.co.uk and local bookshops).
David had previously played with the Egremont band Necromandus who had supported Black Sabbath in the early seventies. The lead guitarist of Necromandus was Baz Dunnery (the brother of Frank Dunnery of "It Bites" one of the most successful Cumbrian bands). Necromandus recorded one album "Orexis of Death" with the support of Tony Iommi.
Mythology were based in Carlisle in the late 60s and from early 1968 featured a lead guitarist called Tony Iommi (who took over from Frank Kenyon) and a drummer called Bill Ward. Tony and Bill were from Birmingham and had previously been in a band called "The Rest" that had decided to move from Birmingham up to Carlisle.
Mythology were a blues/rock band that had some success in the area but eventually disbanded after a brush with the law (allegedly involving cannabis), playing their final gig in Silloth.
Tony Iommi and Bill Ward then returned to Birmingham. There they met up with Ozzy who Tony had known at school (but apparently disliked). In those days Ozzy sported a skinhead hairut! Ozzy and Geezer Butler were forming a band and looking for a drummer. Ozzy asked Tony if he knew any drummers and Tony of course suggested Bill.