Roger Foster said that his family is "disgusted and disappointed" by claims made by a number of women that Savile sexually abused schoolgirls while working at the BBC.
Foster criticised ITV for deciding to produce the programme - which details allegations from the women dating back to the 1970s - and said that he was not only concerned for his uncle's reputation and legacy but also worried about the damage the claims could do to his charities.
"I just get so disgusted and disappointed by it," he explained. "The guy hasn't been dead for a year yet and they're bringing these stories out.
"It could affect his legacy, his charity work, everything. I'm very sad and disgusted."
Foster, from Goole, East Yorkshire, added: "I just don't understand the motives behind this... I think it's very, very sad you can say these things after someone's died and the law says you can't defend yourself when you're dead."
ITV has claimed that some contributors said they were too frightened to speak out while Savile was alive. One woman has alleged that she was raped by him, while another told documentary-makers that she met the presenter at a school in Surrey when she was 14 and was assaulted in his caravan while it was parked in the school grounds.
Today (September 30), the BBC issued a statement following reports that the behaviour by Savile was an "open secret" at the corporation.
"The BBC has conducted extensive searches of its files to establish whether there is any record of misconduct or allegations of misconduct by Sir Jimmy Savile during his time at the BBC," it read. "No such evidence has been found."
The corporation added that "it is simply not possible... to take any further action" with an "absence of evidence of any kind".
Newsnight editor Peter Rippon also explained why an investigation into Savile by the BBC Two programme was never broadcast.
"It is absolutely untrue that the Newsnight investigation was dropped for anything other than editorial reasons," he said, referring to allegations that the corporation tried to instigate a cover up.
"We have been very clear from the start that the piece was not broadcast because the story we were pursuing could not be substantiated. To say otherwise is false and very damaging to the BBC and individuals.
"The notion that internal pressure was applied appears to be a malicious rumour."
Sir Jimmy Savile - who presented shows including Top of the Pops and Jim'll Fix It - died last October at the age of 84.
A complaint about the TV star was made to Surrey Police in 2007, but following an investigation, no further action was taken. He was never charged with any abuse offences during his lifetime.
Exposure: The Other Side of Jimmy Savile is due to air on ITV1 at 10.30pm this Wednesday (October 3).
Photo gallery - Sir Jimmy Savile:
Copyright: flickr/BBC Pictures