Stop any person over the age of 15, on any street, in any country in the world and ask him if he knows who The Beatles are. Then do the same random sampling for any of the other bands mentioned above. The Rolling Stones will come close, but EVERYONE knows The Beatles. They are, after all, more popular than Jesus Christ.
The Beatles, The Rolling Stones, Led Zeppelin, Black Sabbath, The Sex Pistols, U2.
The Beatles are not just the most influential band from the UK, but the most influential band in the history of recorded popular music.
Famous does not necessarily mean influential.
Although the Yardbirds produced three very seminal guitarists, they were not really that influential as a band in themselves. How many Yardbirds songs would the average person be able to name? How many can you name?
I think Cream and Led Zeppelin (not to mention Hendrix and Sabbath) were more important to the development of hard rock than the Yardbirds were, and I think Clapton and Page would have gone in that direction regardless of having been in the Yardbirds. The fact that Clapton, Beck and Page all played in the 'birds is more of an interesting coincidence than a statement about the band as a real force in itself. It had its day and it was somewhat influential, but on the level with Zeppelin or Cream – no way.
I can’t find a cite but I know I read once that the Beatles are the biggest single show business act in history. Could that be true? I can’t give the parameters of the ranking and I don’t remember how trustworthy the publication was, so maybe someone could help out.
Leaffan mentioned everyone over 15 having at least some familiarity with the Beatles. My gut feeling is, that is not far from being true. What always surprises me is how many young people like the Beatles and will freely admit they were the greatest band. And they’re considerably more than one generation removed. It’s so nice to have my own opinion corroborated by the very demographic who normally would make a point of not caring less about a previous generation’s idols. I know I felt that way concerning anything that came before rock and roll, and rightfully so; the pop that came before was inferior. The Beatles transcend the generations and you don’t really have to try to convince anyone they were the greatest.
Uh… U2 aren’t British.
Half the band were born in Britain.
I’m counting the whole UK. The OP asked about bands “across the pond,” and didn’t really specify that it had to be Great Britain. If the OP doesn’t want to count Ireland, though, then I’ll withdraw U2.
The Rutles.
I think it was because of the trousers.
‘The whole UK’ doesn’t cover the Republic of Ireland. Edit: I like this diagram 
Anyway the Rolling Stones never influenced anyone - they were always followers - the usual US blues merchants, a bit of post-Beatles copycat psychedelia. A good band though, but hardly pioneers.
I think the Stones influence was more stylistic than musical. They introduced hedonism and swagger and kind of set the template for arena rock stage shows. I think Jagger was the first guy to take his shirt off on stage, and even if he wasn’t, he popularized it.
ETA as for the statement that they “never influenced anyone,” musically, I beg to differ. They were big influences on Aerosmith and Guns 'N Roses just to name a couple.
Absolutely, and that’s pretty much the same schtick they’ve been doing since 1972?
Yeah, like many here have already stated, The Beatles.
No defense is really necessary…
Pink Floyd #2, IMHO.
Incredible variety this band had.