The song was riding at number three on Friday, closing the gap on the chart leader but behind by around 12,000 copies.
But the publicly-funded BBC, the world's largest broadcaster, said it would play a brief extract on Sunday's Radio 1 chart show -- the traditional slot where the weekly charts are revealed -- following complaints that it was tasteless and offensive.
Radio 1 controller Ben Cooper said he had been "caught between a rock and a hard place" over the decision.
"Nobody at Radio 1 wishes to cause offence but nor do I believe that we can ignore the song in the chart show."
The BBC's new director-general Tony Hall said: "I understand the concerns about this campaign. I personally believe it is distasteful and inappropriate.
"However I do 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.
"We have agreed that we won't be playing the song in full, rather treating it as a news story and playing a short extract to put it in context."
Fans of the Conservative titan have launched a counter-campaign encouraging people to download an obscure punk song called "I'm In Love With Margaret Thatcher".
Thatcher's supporters had deplored the campaign to get the song to number one, and urged the BBC not to play it ahead of her high-profile funeral at St Paul's Cathedral next Wednesday.
"This is an attempt to manipulate the charts by people trying to make a political point," said Conservative lawmaker John Whittingdale, who chairs parliament's Culture, Media and Sport committee.
"Most people find that offensive and deeply insensitive, and for that reason it would be better if the BBC did not play it," he told the Daily Mail newspaper.
He later backed the way the BBC had decided to handle the issue.
The right-wing Daily Mail and Daily Telegraph newspapers led the call to have the song banned by the BBC.
The Mail called it an "insult to Maggie".
Songs previously banned by the BBC include "Je T'aime... Moi Non Plus" by Serge Gainsbourg and Jane Birkin (1969), "God Save the Queen" by the Sex Pistols (1977) and "Relax" by Frankie Goes to Hollywood (1983).
Baroness Thatcher has proved as polarising in death as she was in life.
The state is sparing no expense on her funeral with world leaders past and present on the 2,000-strong guest list, including Queen Elizabeth II and all surviving US presidents.
But opponents of Thatcher, whom they accuse of damaging British industry and society with her free-market economic policies, staged rowdy parties on the night of her death.
Her official biographer Charles Moore, whose authorised account of her life will be published immediately after the funeral, accused the BBC itself of trying to promote the song.
Conservatives have long claimed the British Broadcasting Corporation has a left-wing bias, which the broadcaster denies.
Moore, a former editor of The Daily Telegraph, said that because of her role in the defeat of the communist "Eastern bloc" led by the Soviet Union, Thatcher was more like the heroine Dorothy in the 1939 classic movie than the witch she defeats.
"The reason that song is sung, I think, is that the witch that's dead is the Wicked Witch of the East," he said in a BBC television debate.
"And it was Mrs Thatcher who defeated the east, and in this tale and this song Mrs Thatcher is Dorothy."
Thatcher has long inspired creative anger against her policies.
Primal Scream lead singer Bobby Gillespie told AFP in an interview he was delighted to hear of her death.
"I was very happy when I heard the news," the Scottish singer said in Paris.
Gillespie, 51, the son of a trade union official, said Thatcher's policies had profoundly shaped modern Britain.
"Really, she's not dead, she's just gone," he said.
"Because the policies she put into practice -- privatisations, attacks on the welfare state, attacks on (the) health (service), attacks on the educational system, basically her war against the working class -- these policies have been living (on)."
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