The BBC has said it will not play Ding, Dong the Witch is Dead in full during this weekend's chart show, replacing it instead with a short clip of the song.
In a statement, the corporation said: “The BBC finds this campaign distasteful but does not believe the record should be banned.
"On Sunday, the Radio 1 Chart Show will contain a news item explaining why the song is in the charts during which a short clip will be played as it has been in some of our news programmes.”
In a blogpost, Ben Cooper, the controller of Radio 1 said he felt caught between "a rock and a hard place."
"I find the campaign to promote the song in response to the death of Baroness Thatcher as distasteful as anyone and I’ve thought long and hard about how to respond.
"On one side there is the understandable anger of large numbers of people who are appalled by this campaign.
"On the other there is the question of whether the chart show – which has run since the birth of Radio 1 in 1967 – can ignore a high new entry which clearly reflects the views of a big enough portion of the record buying public to propel it up the charts. Above all, in the middle of this furore is a grieving family."
He continued: "Nobody at Radio 1 wishes to cause offence but nor do I believe that we can ignore the song in the chart show, which is traditionally a formal record of the biggest selling singles of the week. That in turn means that all songs in the chart become an historic fact.
"I’ve therefore decided exceptionally that we should treat the rise of the song, based as it is on a political campaign to denigrate Lady Thatcher’s memory, as a news story. So we will play a brief excerpt of it in a short news report during the show which explains to our audience why a 70-year-old song is at the top of the charts.
"Most of them are too young to remember Lady Thatcher and many will be baffled by the sound of the Munchkins from the Wizard of Oz.
"To ban the record from our airwaves completely would risk giving the campaign the oxygen of further publicity and might inflame an already delicate situation."
Speaking on Radio 5 Live, Cooper said: "It is our duty to inform and educate our audience about this campaign but we can do that through journalism rather than playing 52 seconds of the track."
And asked if he would play any of the pro-Thatcher songs currently being touted for the charts, Cooper said: "That's a decision not make when I see the chart run down in full on Sunday."
The song was at number three this morning having sold about 12,000 fewer copies than the current chart-topper Need U (100%) by Duke Dumont, but with the final sales not coming in until midnight tomorrow, it could still take top spot.
Earlier, one of Britain's most controversial right wing politicians has said the BBC should play the anti-Thatcher anthem Ding Dong The Witch Is Dead on Radio One.
Ukip leader Nigel Farage, who is quoted in the Daily Telegraph, said: “If you suppress things then you make them popular, so play the bloody thing. If you ban it it will be number one for weeks.
“Personally I think that the behaviour of these yobs - most of whom weren’t even born when Lady Thatcher was in power - is horrible, offensive and disgusting.
“Much as I hate it, I think that if you ban a record you make a huge, huge mistake.”
A growing number of Tory MPs have also joined calls for the song, which has quickly become the most talked about issue surrounding Thatcher's funeral.
Yesterday the BBC came under increasing pressure to say whether it will play a song pushed into the charts by people celebrating the death of Margaret Thatcher.
The Wizard of Oz track, sung by Judy Garland, is on course for a top five place after selling 20,000 copies since her death on Monday.
Tory MP John Whittingdale, Thatcher's former political secretary and chairman of the Commons Culture, Media and Sport committee, said it could present a "difficult" dilemma for the BBC.
Whittingdale told The Huffington Post UK: "I very much hope the issue will not arise, in that I would be very saddened if a song which will be being promoted on the basis of celebrating the death of Margaret Thatcher should achieve success that would be sufficient to put it into the charts.
"I think it would be difficult if that were the case, but I hope we're talking about an academic issue, not an actual one."