They were British of Irish origin. Shane lived in London.
j
Can if you like, I guess.
j
To my mind, The Beatles and The Rolling Stones kind of transcend this kind of list, because of the seismic impact of their careers. Handicapping myself by leaving them out, my top six would be:
The Kinks
The Clash
The Jam
Roxy Music
Joy Division/New Order (can’t really separate those)
Mott the Hoople
The Move
The Who
Stackridge
Queen
Genesis
Celia & The Mutations
That Robert Fripp vehicle known as King Crimson by a freaking longshot
Beatles
Napalm Death
Extreme Noise Terror
The Fall
XTC
oh heck why not two more - Carcass, Gang of Four
In our collective defense, after the first 2 posts it became kinda difficult. We should try "Best six excluding …B, S, W, K, PF, LZ
Just an observation …
Notable omissions:
Dire Straits
The Police
Others?
j
Dr. Feelgood? 
Good call!
j
If you want a dark horse, I would add Wire in there and take out, I dunno, the Stones or the Who for my list, both of which I don’t listen to much at all.
With all the hubbub over the recent reunion/tour announcement I’m surprised Oasis hasn’t been mentioned. (Not a fan, but I know they have a big following)
Again, excellent call.
j
Prefer bands - and not solo performers or solos in various bands.
I guess it depends on how you want to define “greatest” bands.
There is no doubt the Stones or The Who blow Wire out of the water when it comes to their impact on music over the last 50 years.
You might like Wire more than those two…you might even argue it is better music. But they come nowhere close to the effect the Stones and The Who had on popular music.
And that is how I was originally answering the question – as “objectively” as possible. It’s my re-read of the OP and “According to YOU” and the OP’s hope to discover some bands they missed that made me update my choice (though Wire will be a hard sell for most people, I think.) My Bloody Valentine would also be on my list, but was already mentioned. And definitely The Smiths.
Which is why I left it open to interpretation. If someone really loves a band to the point it over-rides what they feel is another band’s impact, I want to hear about it.
Personally, I think that that would be hard to do with the Beatles or the Stones.
And in that spirit I recommend London Grammar to you. They are blindingly good.
j
I think Depeche Mode then needs to be in this discussion.
(I’m surprised they have not been listed yet.)
Fairport Convention
Renaissance
Pentangle
King Crimson
Roxy Music
Rolling Stones
And on your recommendation, I watched a couple of their videos. They are very good. I will check out more when I get home.