In 1985, New York radio station WNEW-FM 102.7 did a "Top 1027 Songs of All Time", compiled by listener votes alone. So no music critic snobbery, this was what greater NYC thought were the best songs, as of that time.
Then they played all 1027 songs in a row, from 1027 down to #1. (I remember I was parking my car at LaGuardia Airport [dropping off my sister for college? I forget] as the countdown got to #29, "Roundabout" by Yes. [Given the length of "Roundabout", I think I was able to accompany sis into the terminal, find her flight on the board, point her to the departure gate, say goodbye, and be back in the car before the song ended, but I may be misremembering that part.]) Actually, it turns out that there should have been 1029 songs played, as due to an error, the songs that got enough votes to place at #11 ("Won't Get Fooled Again" by The Who) and #18 ("Freebird", Lynyrd Skynyrd) were omitted from the original "official" list. (Oops. And I wouldn't have liked to be the intern getting all the "Where the FUCK is 'Freebird'???" calls, I'm sure.)
However, the error meant that Zep got to both open and close the show, with #"1027" (actually 1029; from here on I will list all numbers as if the two omitted songs had been included) being "In the Evening" and #1 being, of course, "Stairway to Heaven".
#2-"Born to Run", Bruce Springsteen and the E Street Band #3-"Layla", Derek and the Dominos #4-"Baba O'Riley", The Who #5…wait for it…
#5-"Kashmir", Led Zeppelin
Yes, Zep was so beloved that they took two of the top 5 places in a "Best Songs of All Time" poll in the biggest city in the country. (Despite a very Springsteen-heavy, regional pride vote in the results.) In contrast, the much-beloved-in-Britain "Bohemian Rhapsody" trudged in at a pedestian #236, behind "Allison" by Elvis Costello and edging out "You're So Vain" by Carly Simon. (Queen's flat-out awful 1982 album "Hot Space" had killed off most of their American fanbase and while 1983's "The Works" had kept them going in the UK and Europe, they were a dead issue in the U.S. at this point. Probably some of this was homophobia as well, as Freddy's closet was more and more made out of glass at this point.) As for the Journey fan who posted upthread, although Steve and the boys were not far from their commercial peak, their highest posting was at #123, with "Faithfully".
Meanwhile, the Top 100 was littered with Zep songs:
#15-"Dazed and Confused" #27-"Whole Lotta Love" #42-"Rock and Roll" #50-"All of My Love" #77-"Thank You" (that's a surprise, IMO) #92-"Black Dog"
At one point I was going to do a comprehensive analysis of the list (that's why I've held onto it for 28 years, after all) but I never got around to it. Still, I would venture that Zepp has the most total songs, as well as #1. Even though I've always tended more to the opera/music hall-influenced side of rock (Who, Kinks, Queen, Deep Purple, prog bands) than the "pure" R&B types (Stones, Zepp, etc.), I admire the heck out of this accomplishment.
(Don't get me wrong, it's hardly a perfect list, being a product of its times. I mean, there are HUEY LEWIS songs on here, for fuck's sake. Bruce's "Born in the USA" album is way over-represented, and the Live Aid song "We Are The World" places at an IMO unmerited #39. But Zeppelin even benefits from this…in 1985 people were so desperate for fresh material that The Firm [Page's new band] took #65 with "Radioactive", a mostly-forgotten song, and Robert Plant's The Honeydrippers saw their cover of "Sea of Love" ensconced at #243. Kudos, I guess.)
So yes, by 1985, Led Zeppelin and "Stairway" were still the undisputed kings of Rock, by popular acclaim. As for when they reached that pinnacle, exactly, I couldn't say. Perhaps when Wings put out "Silly Love Songs", thus damaging The Beatles' brand? (Thanks a lot, Paul.)