The furore also raised questions about the future of incoming New York Times CEO and former BBC chief Mark Thompson over how much he knew about the shelving of an investigation into the Savile claims.
Savile was one of British TV's best-loved entertainers with his garish tracksuits and ever-present cigar, but since his death in October 2011 his reputation has been destroyed by claims of widespread child sex abuse.
Culture Secretary Maria Miller said that "very real concerns are being raised about public trust and confidence in the BBC", which is funded by a licence paid by every British household that has a television or radio.
But Patten -- the last British governor of Hong Kong before the handover to China in 1997 -- retorted that the BBC took the allegations "seriously" and had set up two independent investigations into the scandal.
"You know how seriously the trust takes the allegations surrounding Jimmy Savile and the need to maintain public trust in the BBC," he said in his letter.
"I know that you will not want to give any impression that you are questioning the independence of the BBC."
The BBC trust is responsible for holding the broadcaster, which is nicknamed "Auntie" in Britain, to account on how it meets its public duties as set out by a royal charter.
But it has also historically defended its editorial independence from British governments.
--- NYT to 'aggressively' cover Thompson role ---
Across the Atlantic, Thompson denied having any role in the key moment in the scandal -- the scrapping of an investigation into Savile by the flagship current affairs show Newsnight in December last year.
Thompson, who is due to start at the New York Times next month, told the paper he had heard about the probe from a reporter at a party last December when he was still director general of the BBC and followed up with two BBC News officials.
"I talked to senior management in BBC News and reported the conversation I had at the party and asked was there a problem," he said, adding that he was told the story would not be published "for journalistic reasons."
Thompson, 55, who headed the British Broadcasting Corporation from 2004 to September 2012, said: "There is nothing to suggest that I acted inappropriately in the handling of this matter.
"I did not impede or stop the ‘Newsnight' investigation, nor have I done anything else that could be construed as untoward or unreasonable."
George Entwistle, the current director general of the BBC, appeared before British lawmakers on Tuesday and said he regretted that the broadcaster had dropped the Newsnight investigation.
But he denied that pressure from BBC top management had forced it to do so.
The New York Times confirmed in its story that Thompson would join the company as president and CEO in the week of November 12, though either party could end the agreement at any time.
"It is my belief that there isn't anything in my participation or my role in this story that would impede my ability to join and work with my colleagues at The New York Times," Thompson told the newspaper.
But in a blog on Tuesday, New York Times public editor Margaret Sullivan said the paper must "aggressively cover" Thompson's role in what happened at the BBC.
"It’s worth considering now whether he is the right person for the job, given this turn of events," she said.
British police have launched a separate criminal investigation into the alleged abuse by Savile, and Scotland Yard says it believes there may have been as many as 200 victims.
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