Police have announced the search for Muriel McKay's remains was 'unsuccessful' 55 years after her murder.
Detectives said they have found 'no evidence relating to her kidnap and murder' after they ruled out flying her killer over from Trinidad to join dig at the Hertfordshire farm.
Around 20 forensic and specialist officers were involved in the operation at Stocking Farm in Hertfordshire, acting on new information provided by one of her murderers.
Mrs McKay's family have been calling for the police to allow convicted killer Nizamodeen Hosein to be brought to the excavation site to show detectives where he buried her body in 1970. They believe her body cannot be found without him.
They slammed the search as 'nonsense' and 'pointless' without Hosein being there, calling it 'the blind leading the blind'.
It is the third search of the farm and the Metropolitan Police, who are carrying out the operation with Hertfordshire Constabulary, have warned it will be the last attempt to find Mrs McKay.
Police have announced the search for Muriel McKay's remains was 'unsuccessful'
Blue police tents in the garden of Stocking Farm, formerly known as Rooks Farm, where police dug for the remains of Muriel McKay
Muriel McKay's daughter Dianne (left) travelled to Trinidad with her son Mark Dyer (right) to speak with one of her mother's killers, Nizamodeen Hosein (centre)
Police ended the fresh dig for the remains of murdered Muriel McKay Stocking Farm in Stocking Pelham, Hertfordshire (pictured)
The 55-year-old vanished on December 29, 1969, after two brothers mistook her for the then wife of media tycoon Rupert Murdoch.
Hosein and his brother Arthur demanded £1 million – the equivalent of £20 million today - for her safe return to Alick McKay, a deputy to Mr Murdoch at News Limited.
There were two botched attempts to pay some of the ransom – believed to be the first incident of its kind in the UK – and Mrs McKay was never seen again.
The Hosein brothers were later caught and sentenced to life for murder in 1970 despite the absence of a body – another gruesome legal first.
In a letter to the murdered woman's family, Katherine Godwin, Detective Superintendent in the Met Police, said: 'We have now completed the search of the area set out in the agreed parameters, along with an additional strip which we identified was not covered by the 2022 search or the 2024 parameters.
'I am so sorry to say that the search has not been successful in finding Muriel's remains or any evidence relating to her kidnap and murder.'
Searches took place at the farm around the time of the murder and again two years ago, when ground penetrating radar and specialist forensic archaeologists were used but no body was found.
Arthur died in prison in 2009 and his brother was deported to Trinidad and Tobago after serving his time.
Muriel McKay's son Ian (right) and her grandson Mark Dyer (left) spoke to the press as they joined police in the search for her body at Stocking Farm in Hertfordshire
Muriel McKay's son Ian McKay (Right) and her grandson Mark Dyer who have visited the farm
Brothers Arthur (left) and Nazamodeen Hosein (right) were found guilty of her murder. Arthur died in prison in 2009, while Nizam was deported after serving a 20-year-prison sentence
Last December the 76-year-old provided new information about Mrs McKay's whereabouts after he was visited by her daughter Dianne, 84, and grandson Mark Dyer, 59.
He claimed she died from a heart attack after seeing a television appeal from her family.
The family campaigned for two years to persuade the Met and the farm's owners to approve another search of the area.
Earlier today, Hosein, who lives in Trinidad after being deported at the end of his sentence, said he would get on a plane 'tomorrow' to assist in locating the burial site.
He claimed a successful search would be 'more or less impossible' without him present after flying him over was previously ruled out.
Speaking in a series of videos, Hosein said: 'I'm quite willing to come to England tomorrow. To help the search for her body.'
Asked if he would help, Hosein added: 'Every which way.'
Mrs McKay's daughter Dianne, 84, visited Hosein in Trinidad in January and he told her he remembered where he had buried her mother: three foot from a fence at the farm.
The murdered woman's son Ian McKay, 82, flew over from Australia, where he now lives, to join the search, and her grandson Mark Dyer, 59, had also joined.
Mr McKay said on Sunday that the family was frustrated that this had not happened.
He said: 'The whole thing is a no-brainer. You wouldn't go and dig for treasure (without) the person who buried the treasure telling you where it was.
Police searched the farm in 2022 (pictured), but Hosein claims they looked in the wrong area
The abduction is believed to have involved a case of mistaken identity - with the kidnappers intending to seize Anna Murdoch, the former wife of media tycoon Rupert Murdoch (pictured)
'It doesn't make sense. It's almost pigheadedness. We keep on being fobbed off.'
Last week, Mr McKay also criticised the police for allegedly 'ignoring Nizam's specific information' of where his mother is.
He added: 'It seems to me a nonsense that Nizam is not here.
'The fact he's a convicted criminal is hard for us to swallow but he has served his sentence.
'Why would you not have the man who has now admitted to burying her here to help find her?'
Muriel's grandson Mark Dyer added that the dig was like the 'blind leading the blind' and that Hosein could be brought over on the next flight.
He said: 'The whole thing is very kind but pointless without the perpetrator.
Police seen at Stocking Pelham in Hertfordshire where they searched for her remains
Around 20 officers from the Met and Hertfordshire Constabulary searched for her body
'He's a plane ticket away from ending the misery forever. Is she there or isn't she there?'
The Met Police said previously that it was discussing Hosein's position with the McKay family.
A spokesperson said: 'Bringing Hosein to the UK was carefully considered prior to the search and we did not believe it would provide us with any further or useful information.
'Therefore, we did not formally approach the Home Office, who would be required to grant permission.
'We understand the family believe Hosein attending the search would be useful and we continue to liaise and discuss this with them.'
The Metropolitan Police had previously told the family that it was considering cooperating with Hosein in the fresh hunt but the decision would rest with the Home Office, because he had been deported.