Girlschool, an all-female New Wave of British Heavy Metal band, is credited as being the longest-running all-female rock band, going strong since 1978. They came along basically right around the same time The Runaways were breaking up. Girlschool filled the all-female hard rock band void admirably by playing the aggressive combination of hard rock, metal, and punk we have come to expect (and love) from NWOBHM bands.
The band had some pretty solid success in the UK, headlining medium-sized arenas and festivals. They also toured with the likes of Iron Maiden, Scorpions, Motörhead, Uriah Heep, Rainbow, Black Sabbath, and Rush in the early '80s. Their first three albums made the Top 30 on the UK albums charts, with their second album (Hit and Run, released in 1981) reaching #5.
I particularly enjoy their "Headgirl" collaboration with Motörhead, 1981's St. Valentine's Day Massacre, a 3-song EP on which the bands played one song together (a cover of Johnny Kidd & The Pirates' "Please Don't Touch"), Girlschool covered a Motörhead song ("Bomber"), and Motörhead covered a Girlschool song ("Emergency"). That EP hit #5 on the UK singles chart. (Here's a link to a performance of "Please Don't Touch" on German TV.)