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Clarkson, 54, was called before BBC bosses this week after the Mirror newspaper reported he was heard using the word "nigger" as he recited an old version of the rhyme "Eeny, Meeny, Miny, Moe" to choose between cars in filming two years ago.
The newspaper did not say how it got hold of the footage, which was not aired, but the revelation led to calls for Clarkson to resign or be sacked from the BBC, which is funded by a licence fee paid by all UK households who own a television.
The presenter, known for his humorous but blunt style, apologised in a video on Twitter on Thursday, saying he tried to avoid the racist expression by mumbling over that part of the rhyme in two takes and replacing it with "teacher" in a third.
But in a regular column in the Sun newspaper on Saturday, Clarkson admitted he was on his final warning from the BBC after the latest controversy to hit the outspoken but highly profitable presenter.
"I've been told by the BBC that if I make one more offensive, remark, anywhere, at ay time, I will be sacked," wrote Clarkson, insisting he had not used the 'n' word that he found "extremely distasteful".
"It's funny. I've always thought I'd be sacked for something I said. Not for something that actually, I didn't say."
SERIES OF CONTROVERSIES
The furore comes just days after Top Gear producers apologised for a "light-hearted" joke by Clarkson in Myanmar and Thailand in which he referred to a "slope" on a bridge as an Asian man crossed a makeshift structure built by the presenters.
The show prompted complaints of racism and producer Andy Wilman apologised, saying they were unaware it was a racially offensive term for Asians used in countries like Australia and the United States and regretted any offense caused.
The BBC has regularly downplayed controversies over Clarkson's comments through the 26-year history of Top Gear, one of its best-selling shows which has aired in 214 countries, helping make Clarkson, a journalist by background, into a global celebrity.
Top Gear was named by Guinness World Records as the world's most widely watched factual TV programme in 2013 and its popularity has led to spin-offs including video games and a magazine.
But Clarkson's strong views have pitched him up against politicians, national governments, environmental groups, car companies and communities across Britain over the years. Facebook has an "I Hate Jeremy Clarkson" page.
A BBC statement on Thursday said the corporation had spoken to Clarkson and made "absolutely clear" the standards expected.
"We have left him in no doubt about how seriously we view this," said the statement.
A BBC spokesman said on Saturday the corporation had nothing to add beyond this statement. The BBC declined to say how much Clarkson makes or how much Top Gear earns.