Unionists were outraged after the BBC played a segment from The Roll of Honour, which remembers the lives of 10 republicans who died during the Maze Prison hunger strikes in 1981, on their Sunday chart show.
The song was banned at football matches in Scotland – prompting angry Celtic fans to launch a campaign to get the song into the top 40. Originally released in 1982, the song's lyrics brand England "a monster" and laud IRA hunger striker Bobby Sands as "gallant" and "brave".
BBC Radio 1 played the first line of the song after the show's presenter Jameela Jamil explained the protest song was a chart entry as a result of a campaign by Celtic supporters opposed to the Offensive Behaviour at Football and Threatening Communication (Scotland) Act.
The lyrics played on air stated: "Read the roll of honour for Ireland's bravest men, We must be united in memory of the 10."
Unionists had called on the BBC to ban it from the airwaves, as they said it glorified terrorism.
A BBC source said: "We believe it would be wrong to ban the song outright as free speech is an important principle and a ban would only give it more publicity."
DUP MP Gregory Campbell wants the song to be banned.
He said there was a duty for the BBC as a public service broadcaster not to broadcast material promoting terror.
"If the BBC was faced with any other song that commemorated murder, and on occasions multiple murders of innocent people, they would take an executive decision not to promote such a recording," he told the Belfast Telegraph.
"Exactly the same principles should apply to this as would if it were al-Qaida, Basque separatists or any of the other Middle-Eastern terrorist groups."
Ulster Unionist MLA Tom Elliott said: "I would ask that the BBC does not play this song because it glorifies terrorism and is highly offensive."
It is understood that a clip of the instrumental intro and the first two lines will be played on Sunday if the song remains in the Top 40.
A BBC source told the Belfast Telegraph: "We believe it would be wrong to ban the song outright as free speech is an important principle and a ban would only give it more publicity."
First released in 1982, The Roll Of Honour by The Irish Brigade describes the hunger strikers as "martyrs" and "the bravest of the brave".
The Irish Brigade was asked by supporters group Fans Against Criminalisation (FAC) to cover the song to highlight opposition to the Offensive Behaviour at Football and Threatening Communication (Scotland) Act.
A statement from Fans Against Criminalisation said: "We urge the Celtic support to download this song to embarrass those who seek to criminalise us to demonstrate that we stand by those who are being arrested at their homes and dragged through the courts and that we will not tolerate the continual harassment of our fellow fans at the hands of Police Scotland."
A statement from The Irish Brigade, said: "It was an honour and privilege to be asked by Celtic Fans Against Criminalisation to permit them to promote the song The Roll Oof Honour to aid the funding of their campaign against the law that affects everyone with Irish roots or a love of Irish culture."
The band denied the song was sectarian.
Celtic FC did not respond to requests for comment.
Roll of Honour lyrics
Read the roll of honour for Ireland’s bravest men
We must be united in memory of the ten,
England you’re a monster, don’t think that you have won
We will never be defeated while Ireland has such sons.
In those dreary H-Block cages, ten brave young Irishmen lay
Hungering for justice as their young lives ebbed away,
For their rights as Irish soldiers and to free their native land
They stood beside their leader – the gallant Bobby Sands.
Now they mourn Hughes in Bellaghy,
Ray McCreesh in Armagh’s hills
In those narrow streets of Derry, they miss O’Hara still,
They so proudly gave their young lives to break Britannia’s hold
Their names will be remembered as history unfolds.
Through the war-torn streets of Ulster the black flags did sadly sway
To salute ten Irish martyrs the bravest of the brave,
Joe McDonnell, Martin Hurson, Kevin Lynch, Kieran Doherty
They gave their lives for freedom with Thomas McElwee.
Michael Devine from Derry you were the last to die
With your nine brave companions with the martyred dead you lie
Your souls cry out: “Remember, our deaths were not in vain.
Fight on and make our homeland a nation once again!”
The Roll Of Honour, an Irish rebel song, was recorded by The Irish Brigade in the 1980s. The band, from Co Tyrone, formed after the 1981 hunger strike. The song was also covered by the Wolfe Tones. It is associated with the hunger strikes, when 10 republican prisoners died at the Maze.