They were drawn up in 2012 after a number of people who have loved ones buried nearby complained to cemetery bosses about having to share the graveyard with the paedophile.
Savile’s family gave the move the green light, while Scarborough Cemetery in North Yorkshire has said ecclesiastical consent will not be a problem.
However, the plans were halted at the last minute because trustees of the Jimmy Savile Charitable Trust did not want to pay the £20,000 cost.
The cash, the trust argued, was supposed to be going to good causes. Only the headstone has been removed, but the plans for an exhumation remain filed with the undertaker.
Scarborough councillor Colin Haddington, who has led calls for an exhumation, said:
“Jimmy Savile will be on people’s minds every time they lay flowers no matter how long it goes on.
“It would be better for everyone if he was dug up and cremated.
The undertakers visited the family in 2012 and the family agreed to the exhumation plan but then the trust refused to release any money to pay for it.
“I can understand the trust wanting to use the money to pay compensation to the victims but it is just as important for the families who have loved ones buried there.
“It would be nice to think if there was anything left from his estate it would be enough because it should be done.”
Savile died in October 2011 aged 84 and was buried in a quiet spot overlooking the North Sea.
The 6ft-wide triple plot, filled with two and half tons of reinforced concrete, had steel bars inserted to deter grave robbers.
All that was buried within his gold coloured coffin, however, were his Royal Marines green beret and medal, rosary beads, a Help For Heroes wristband and a couple of his trademark cigars.
Sources said the charity reluctantly signed off on the disgraced DJ and television presenter’s lavish funeral arrangements three and a half years ago.
They also drove a hard bargain over the headstone encryption, forcing undertakers to carve “It was good while it lasted” largely for free.
The gaudy £4,000 triple headstone was removed in 2012 with work starting at midnight and finishing a few hours later.
Removing the coffin would take much longer and involve closing the graveyard for two days, the council plans show.
Among those in favour of exhuming the former Top of the Pops presenter was his nephew Guy Marsden.
He previously told Sky News: “If it is causing heartache and pain we would definitely go along with the people of Scarborough and the people whose loved ones are buried there.
‘My view, and I could say that of a lot of my family, would be that if it comes to it where he has to be moved, let’s get it moved. Let’s get it done.”
The Jimmy Savile Charitable Trust refused to comment.