Product placement or commercial issues can trigger bans too
“Lola” - The Kinks
An initial ban for this 1970 song caused a round trip across the Atlantic for songwriter and lead singer Ray Davies. In the original recording, the lyrics referred to Coca-Cola, a product placement which was heavily frowned upon and contravened the strict BBC rules.
Davies hastily reworded to Cherry Cola but had to fly back from the US, where The Kinks were on tour, to London so he could re-record the single for release. Today's technology could have had that fixed in an hour, but the urgent flight was the only route to a quick fix back then.
“Radio Radio” - Elvis Costello and the Attractions
In an odd quirk, this is about a song that did get played. Much to the fury of Saturday Night Live and its producer, Loren Michaels. The ban went instead to the singer. Elvis Costello and the Attractions were a late call-up for the TV show, replacing the Sex Pistols.
It was a big break in the US for Costello and the band, but after just a few bars of “Less Than Zero” Costello called a halt on live TV and switched to a different song “Radio Radio”. The lyrics for that are very critical of the way TV and radio are highly commercialized and corporate controlled. It was very much a song that SNL, Lorne, and NBC weren't happy for us to hear. Costello was banned from the show, eventually making a second appearance 12 years later.