Lord McCluskey said he was also shocked to hear that Robert Henderson QC had been accused of repeatedly sexually abusing his daughter from the age of three.
Susie Henderson has waived her right to anonymity to tell of her alleged ordeal at the hands of her father and several other prominent figures, including senior Tory MP Sir Nicholas Fairbairn.
The 48-year-old claims she was repeatedly subjected to sickening sex attacks by her father, who was well known and respected in Scotland's legal fraternity.
She also alleges that she was passed among a number of his colleagues who also attacked and raped her at the family's Edinburgh home.
Lord McCluskey, a former Solicitor General for Scotland, said he found the claims hard to believe.
The former judge, who wrote a glowing obituary for Mr Henderson following his death in 2012, said: "I'm utterly flabbergasted by these allegations. Never in my life have I heard any suggestion of anything of this kind involving Bob Henderson.
"I'm just amazed to hear it and I would be astonished if it turns out to be true.
"I've no reason to believe it's true - I have no evidence and I never heard even a bit of gossip suggesting this.
"I would await the outcome of any inquiry before adding anything further."
Miss Henderson's case was looked at by police in 2000, but was halted after details were leaked to the press. She said officers had told her that nobody would know until the investigation was over, but panicked and refused to continue when details appeared publicly.
At that time she handed a number of key pieces of evidence over to the police but claims she was recently told that they had been "misplaced".
A number of articles appeared following the initial investigation, but Miss Henderson was referred to only as Julie X and her father's identity was never revealed.
She now wants the case to be reopened by detectives.
"I want it acknowledged that my father and Fairbairn did something very evil," she said. "Not just to me. There are other children out there. And these were people in power. We put them there and they are supposed to be trusted. It's not right."
Miss Henderson also claims to have the names of six other members of the Scottish legal profession who were involved, two of whom are still alive.
Detective Chief Superintendent Lesley Boal said Police Scotland were committed to investigating all reports of historic abuse.
She said: "There are many reasons why a victim may not report such abuse until years - even decades - after the event.
"These can include fear of not being believed, especially if the individual is a prominent public figure, and of reliving the incidents. Similarly, some victims may contact the police to report abuse but then find it too difficult. We will listen, we will ask our partners in support services to assist and we can pick up where we left off when they feel more able to provide the necessary information."
She added: "Any report of historic child abuse will be treated seriously."
Miss Henderson claims that, while her father was seen as a flamboyant star of the legal profession, behind closed doors her had a much more sinister side.
She believes he began abusing her when she was just three and would tell her mother he was taking her for a nap before carrying out the attacks. The advocate also hosted regular parties and Miss Henderson said she was told to do "whatever anybody wanted".
Miss Henderson claims to remember an incident where Mr Fairbairn, a former Solicitor General, raped her when she was just four or five years old.
Mr Fairbairn, who died in 1995, has been linked to the notorious Elm Guest House in London, where young boys are believed to have been plied with alcohol and sexually assaulted. Calls have been made for the Scottish Government to instruct an inquiry into historic sex abuse cases.