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Police have discovered a bone at the site where they were told Muriel McKay's body was buried 57 years ago.
Evacuators working for the family made the discovery about a metre down in the back yard of a betting shop in Hackney, East London.
A forensics team is now analysing the bone, which is about nine inches long and a couple of inches wide, and a murder scene has been declared.
The Metropolitan Police said in a statement: "Police are aware of reports surrounding the discovery of a single bone in the garden of a property in Bethnal Green Road, Hackney. The bone was uncovered during an independent search.
"Officers are now on scene and work is being undertaken to establish the origin."
Muriel's grandson Mark Dyer said: "It would be a great outcome to end this ghastly mystery for our whole family and all of those who've been interested enough to follow our story.
"Four years of intense investigation have led us here and we're waiting to hear if the bone is human. It's been found in a place we were told to look last year."
Muriel was 55 when she was kidnapped by brothers Arthur and Nizamodeen Hosein from her home in Wimbledon just after Christmas in 1969.
She was married to Alick McKay, the deputy to newspaper mogul Rupert Murdoch.
Her kidnappers had mistaken her for Murdoch's wife Anna and kept her hostage in Hertfordshire and demanded a million pounds for her safe return.
The brothers were eventually arrested and convicted at the Old Bailey of Muriel's murder.
It was one of the first murder trials with no evidence of the victim's body and they never revealed Muriel's fate.
The family tracked down Nizamodeen to his native Trinidad five years ago and persuaded him to confess to a crime he had always denied.
Nizam told Diane and her son Mark Dyer that Muriel collapsed and died from a seizure within a few days.
He said he buried Muriel on the farm, pointing to old photographs and maps and indicating a precise spot "three yards from the fence".
This led Scotland Yard to reopen the investigation, with officers carrying out two digs at the farm.
But they found no trace of Muriel and concluded that Nizam was wrong or was not telling the truth.
Following this, the family issued a £1m reward for information last year and were contacted by Hayley Frais in Israel who told them her late father Percy Chaplin ran a tailor's shop in Bethnal Green in the 60s and 70s.
Mr Chaplin made suits for his neighbours the notorious gangster brothers Ronnie and Reggie Kray, but also employed Arthur Hosein, his daughter claims.
On his deathbed, Mr Chaplin allegedly told Hayley that he had a long-held suspicion that a criminal associate of Arthur's dug up Muriel's body at the farm and re-buried it behind his premises, which is now the betting shop.
