According to YOU.
Genre is open. You can judge by music sales, influence on later music or just the awesomeness of their talent. Whatever you feel qualifies them to be deemed the greatest. But only 6 band and a few words to make your case.
I’m hoping this thread will open my eyes to some things I’ve missed. (This weekend I learned about Terry Reid. What an amazing talent - I’d never heard of him.)
So what British bands were the greatest ever?
Well the automatics are The Beatles, The Who and The Rolling Stones*.
So the next 3?
Mine are Led Zeppelin, Pink Floyd and Queen. Make that Yes.
* I’m not even a Stones fan, but to not include them would be nuts.
The Kinks
Queen
Elton John
ETA. I didn’t know Zeppelin was British. TIL
Ok. But this is just, like, my opinion man.
I’m not going to put the obvious ones in - those top 3 listed above, because they’re almost too much a given. Although I’ve never been that much of a fan of The Who.
Queen - One of the greatest live bands ever
Iron Maiden - Another great live band, long career, great metal music
Blur - Best of the ‘Britpop’ bands, whatever Oasis fans might tell you
Paul Weller - Bit of a cheat, because having him lets you include The Jam and Style Council as well as his excellent solo stuff
David Bowie - well, duh
Madness - I’ve always liked them.
In no particular order:
Are we only considering bands? I’d think so, but the answers reveal otherwise.
Kinks for sure.
The last two? For me, it would probably be Sabbath and The Clash.
I’m not sure I would use the term “greatest.” But here are some of my favorites:
King Crimson
The Who
Black Sabbath
Deep Purple
Babe Ruth
Cream
Beatles
Stones
Kinks
Jam
Clash
Faces.
One of these is not like the others.
Cheat or not, an excellent pick.
Man, that’s hard, and though my first four picks are obvious and not very original, quality matters:
The Beatles
The Rolling Stones
The Kinks
The Who
The Clash
The Smiths
ETA: it was extremely tough to leave out Elvis Costello & The Attractions, one of the best bands in the Universe.
I’d go with you, but I think I would replace Yes with the Moody Blues. I’m not even that big a fan of theirs and like Yes they had their share of pretentious drivel. What puts them up top for me is their awesome musicianship. Every time I hear a piece of theirs on the radio I’m struck by just how great the music sounds.
Too bad that Blind Faith put out only one album. It’s one of my all-time favorites. Talk about musicianship.
Speaking of which, what to do about Eric Clapton? He was a member of Cream in 1968, Blind Faith in 1969, and Derek and the Dominoes in 1970. With a backup stint in Delaney & Bonnie and Friends. That stretch is on a top-six list for three years of music. If Paul Weller gets in …
King Crimson? 
I’m not a huge prog fan, but I find some of it quite interesting and intellectually-challenging. Early KC is in this category, for me. 
This is a bit OT, but I find him to be a huge disappointment. I love his work in Cream. His solo work for the past 40+ years? Absolutely boring to my ears. Completely void of imagination; nothing “interesting” or thought-provoking, just “safe” riffs and chord progressions. Not sure what happened. 
Beatles
Stones
ELP
King Crimson
Who (only because of Keith Moon)
Rutles
Beatles
Who
Kinks
Pink Floyd
Led Zeppelin
Stones
Clapton’s music was fantastic and certainly is on the short list when making a list like this.
But he’s such a piece of shit otherwise that makes me struggle to recommend. I started a thread some time ago about whether we can enjoy art by people who are otherwise awful:
I find it interesting that no one mentioned Frank Zappa in that thread. Moon just published a tell-all book. I am not going to read it, because I don’t want his personal flaws to taint my enjoyment of his music.
I would say the automatics are The Beatles, the Rolling Stones, and Led Zeppelin. While I’d include the Who in my 6, I wouldn’t say they’re a sure thing. My last two would be the Kinks and Yes.
The Beatles
The Rolling Stones
Led Zeppelin
Elton John (not a band, but really outstanding)
David Bowie (see Elton John)
The Animals (Yes, not one most people would choose, but Eric Burdon & Co brought a rough edge to the British Invasion and through the 1960s evolved in much the same way the Beatles and Stones did, if a bit unevenly.)
If I had to choose a later band as a Plus-One: The Clash.