Has this already been mentioned - the BBC banned ‘Relax’ by Frankie Goes to Hollywood.
Listening to the lyrics, it becomes obvious why, but i bet most of the time people don’t listen to the words as long as it’s a great song to dance to!
Oh i see it has been mentioned!! 
Yes…but they played it until one of their dj’s refused to do so.
Anything by Judge Dread
Judge Dread had all of his 11 singles that entered the UK Singles Chart banned by the BBC, which is the most for any one artist.
Sexual innuendo said the BBC
Curious to know the name of the DJ concerned, or why the BBC chose not to ban him instead of a really good song.
Mike Read…who may have been on their breakfast show at the time.
I remember sitting in my car after working 2nd shift (I got done at 2AM) and hearing this on my AM radio back in the very early 80’s…and was just…well… 
Ian Dury wrote the song “Spasticus Autisticus” knowing it would cause trouble, and hoping it would be banned. It was written in response to the UN designating 1981 as the Year of the Disabled, as if high-lighting the ‘equalization of opportunities, rehabilitation and prevention of disabilities,’ with a motto that declared “a wheelchair in every home,” would somehow magically bring genuine equality and support where it was needed.
Dury thought the Year of the Disabled was patronizing and ‘crashingly insensitive,’ and his response was to write a song straight from the heart against the naivety and arrogance of well-meaning liberals. ‘Oh, I see, so in 1982, we’ll all be all right!’ Dury said.
The BBC duly obliged
Not just by the BBC
One of the most seemingly innocent songs on this list, “Eve of Destruction” was sung by Barry McGuire and written by P.F. Sloan). It was banned by several U.S. radio stations after the powers that be decided they didn’t like McGuire’s opinions and thought his band was anti-war.
Kodachrome - Paul Simon; Vinyl record “Kodachrome” is a song by the American singer-songwriter Paul Simon. It was the lead single from his third studio album, There Goes Rhymin’ Simon … The song was banned by the BBC because it was a type of film manufactured by Kodak.
No advertising on the BBC
It’s amazing any song made it through that test. So many things are called by their brand name. What if someone said hoovering? That’s a brand name. People say Kleenex here for facial tissues sometimes. Many everyday words are brand names.
Jerusalem is a British national song based on a poem by William Blakeprinted in 1808. At the heart of the poem is the contrast between the harmonious, peaceful society Blake aspired to and the crushing reality of the rapid industrial transformation of his natural world.
Blake was a radical poet and artist who lived most of his life in poverty and obscurity. Like most Romantics, he wrote and poems that celebrated energy, imagination and freedom, but what separated him from the rest were his incredible artistic abilities that allowed him to illustrate his writings.
In 1916, the little known Jerusalem was included in the patriotic anthology The Spirit of Man, edited by the poet Robert Bridges, at a time when the national spirit had hit its low due to the high number of casualties in World War I.
Bridges also commissioned composer Sir Hubert Parry to put it to music, asking him to supply “suitable, simple music to Blake’s stanzas – music that an audience could take up and join in.”
The song was first called And Did Those Feet in Ancient Time, so most of its early scores had this title. Then, in 1922, Sir Edward Elgar re-scored the work for a very large orchestra to perform at the Leeds Festival, and the rest was history.
It is now a popular hymn, sung in churches, schools, and at sporting events across England. For decades, many have considered it to be the unofficial English anthem.
In 1973, progressive rock band Emerson, Lake & Palmer recorded their version of the song, keeping the poem’s title Jerusalem. Though released as a single, the song failed to chart, and was banned from BBC airplay.
Drummer Carl Palmer later expressed disappointment over this decision:
“Jerusalem” has a great story attached to it. It was recorded here in the U.K., and we had to present it to the BBC. The BBC had a panel at the time, and they would veto what would be played on the radio and what could be shown on television, so for us to get the single released, it would have to go in front of this BBC panel, which was about four or five people.
He also added:
So “Jerusalem” was recorded by us, and it was banned immediately by the BBC. We thought it was an unbelievable piece of music. It actually summed up prog rock, British prog rock, in that moment in time. It had everything. It was so grand, it was so English, and it was absolutely perfect for the voice."
An anthem of teenage devotion, The Shangri-La’s’ Leader Of The Pack is a widescreen tale of undying teenage love, motorbikes and death on the streets. Too much of the latter, it appeared, for the BBC, who banned it for its overt references to teenage death. However, there was one occasion when the censors were thwarted. In 1964, a live broadcast of a choir performance at Keele University Chapel was disturbed when Leader Of The Pack was played in the background – a student had placed a record player backstage as a prank. Proof a classic record can never be denied airplay. https://youtu.be/t5vFOpVGjVc?si=UKinqK7Deg6kP_j1
“Statue of Liberty” is a 1978 single by XTC. It was recorded at Abbey Road Studios, London and subsequently banned by BBC Radio 1 for the lyrics “In my fantasy I sail beneath your skirt”.XTC performed the song on the BBC2 television show The Old Grey Whistle Test in 1978.
The Purple Gang are a British rock band active intermittently since the 1960s. They were originally associated with the London psychedelic scene. They released their debut album, The Purple Gang Strikes in 1968, with one track, “Granny Takes a Trip” banned from being broadcast by the BBC.
They thought it was about LSD.
But it was actually about a Boutique of that name…so they would have banned it for advertising!
Proto-electronic outfit The Earthlings from Birmingham were inspired in 1965 by a hot new BBC science fiction show called Doctor Who. The BBC had no objections to the appropriation of the notorious extraterrestrial mutants from the series, but it did take issue with the broadcasting of an SOS in Morse code, which appears about two thirds of the way in. It was decided that the record might be broadcast at a later date if the code was in some way scrambled. Presumably it would have been fine post-1998 when Morse code as a way for ships to Mayday was replaced with a new satellite safety system, though by then it may have lost some of its relevancy.
Someone at the BBC sure was working overtime.
The lyrics to “Peaches” featured coarse sexual language and innuendo to a degree that was unusual for the time. The song’s narrator is girl-watching on a crowded beach one hot summer day. It is never made clear if his lascivious thoughts (such as “there goes a girl and a half”) are an interior monologue, comments to his companions, or come-on lines to the attractive women in question. The critic Tom Maginnis wrote that Hugh Cornwell sings with “a lecherous sneer…spill[ing] into macho parody or even censor-baiting territory”.
The single was a double A-side with “Go Buddy Go”.The latter was played on UK radio at the time and also was performed on the band’s first BBC TV Top of the Pops appearance, because the sexual nature of the lyrics of “Peaches” caused the BBC to censor it. Still, “Peaches” was ranked at No. 18 among the top “Tracks of the Year” for 1977 by NME, and it reached No. 8 in the UK Singles Chart. The radio cut was re-recorded with less explicit lyrics: “clitoris” was replaced with “bikini”, “oh shit” with “oh no” and “what a bummer” with “what a summer”. The catalogue number of the radio version was FREE 4.
The Smoke 'My Friend Jack’ From the opening line of 'my friend Jack eats sugar lumps…', the BBC had cottoned on to the fact that LSD was mainly administered via cubes of sugar, so The Smoke’s reference didn’t stand a chance with the committee.
