To be fair, there’s probably not a large set to choose from, depending on how each poster is defining “greatest,” “British,” and “band.” Historically, there just haven’t been a huge number of successful and/or influential (which is how a lot of the posters are defining “greatest”) British bands which were fronted by women.
Though, that’s not a unique issue to British bands: if one asked the same question about American bands, it’d still be a fairly narrow list. Historically, “bands” (particularly rock bands) were usually groups of guys, and female vocalists were often either solo artists, or vocal-only groups (e.g., the Motown “girl groups”).
And, of course, two of the prominent ones which have been mentioned by others in response to your post – Fleetwood Mac and The Pretenders – are being debated as whether they qualify or not, due to American members (and, particularly, female American vocalists).
And then I can’t really think of any sixth band that I feel rises to that exalted level. GTH I might pick the Kinks, or Queen, or the Buzzcocks, or Sabbath, but it would feel like a “one of these things is not like the others” list. (I would also consider Crass, who haven’t been mentioned here yet)
I saw Renaissance a few years ago, whose singer is Annie Haslam. They were terrific and her voice was still magical. By far the best concert I’ve seen from a 50-year-old band.
Is Renaissance remotely in the running for the 6 greatest British bands of all time? Very good, of course, but not historically great. The only historically great band fronted by a woman in the 1960s was Jefferson Airplane. That’s just a product of the times, not a moral judgement. If people dismiss that era as dinosaur rock, just lift the needle off the record.
I’m prepared to defend Fleetwood Mac as a historically great band fronted by a woman, but not as a British band. I know that Peter Green led the group and wrote such huge well-respected hits in England. But they weren’t yet great, any more than Pink Floyd was historically great with Syd Barrett. Christine Perfect was recruited in 1970 after Green left. American guitarist Bob Welch joined in 1971 and wrote most of their best stuff over the next half-dozen albums, and the band moved their base to California. Then came Buckingham-Nicks and superstardom.
Curved Air came to mind as a British band with a female lead singer, Sonja Kristina. A couple of notable members (and future Rock Hall of Fame inductees) were Stewart Copeland and Eddie Jobson.
I’m having trouble thinking of British bands fronted by women. Seems like women singers are more common in American bands or as solo artists.
If I were ruling, I’d say you could count them as a British band or a female-led band, but not both. (Since Chrissie Hynde was born and raised in America.)