The 55 year old was kidnapped from her house in Wimbledon Village and murdered in 1969 by brothers Arthur and Nizamodeen Hosein.
Martin Brunt says her family are appealing to Met Police commissioner Sir Mark Rowley, to bring back the latter from Trinidad to help with the search.
Detective Superintendent Katherine Goodwin, Specialist Crime, said: “After eight days of searching unfortunately we have not been able to find Muriel’s remains. We all shared a hope and desire we would find her burial site and bring some closure to her family and I am so sorry we have not been able to do that. This is not the outcome any of us wanted.
“Since the beginning of last week, a team of detectives and specialist search officers have been working at the Hertfordshire farm where it is thought Muriel may have been buried to carry out meticulous and detailed work to find her.
“The parameters for the search were set following very careful examination of all the evidence and information gathered by the investigation team, which included speaking to Muriel’s family and interviewing Nizamodeen Hosein in Trinidad. We are extremely grateful to the property owners for allowing us to search the land, causing considerable disruption to their daily lives.
“We have searched all the areas identified as the possible site for Muriel’s remains, including all of the former manure heap, and far beyond. This follows a search carried out at the farm in spring 2022 which unfortunately was also unsuccessful. We can conclusively say the information given by Hosein in the last two years is not correct, Muriel is not at the location he has indicated.
“We know questions have been raised about why we have not brought Hosein to the UK to assist with the search. Our view has always been that we do not believe it would provide us with beneficial information and therefore we would not formally approach the Home Office who would be required to grant permission.
“We carefully reviewed this decision during the search and, based on Hosein’s reliability as a witness and the likelihood of a successful outcome, we stand by our original decision.
“As we have said previously, Muriel’s family are aware it would not be proportionate to carry out any further searches and that our investigation is now at an end. We are saddened that we were unable to bring them the closure they so desperately long for.”
The property owners said: “It is a very disappointing result not to have found the remains of Murial McKay. We granted permission for the dig in our garden, to support the family of the deceased to find closure to this tragic event, despite the evidence provided by the murderer being inconsistent and unreliable.
“The murderer provided guidance that he had buried the body at a certain spot, acknowledged by the family of the deceased. We are pleased that the family of the deceased attended the dig on multiple occasions to witness the professionalism, dedication and hard work of the police in excavating an area in excess of 250 sq m around the spot agreed by all parties.
“We have been told by the police that they have completed their search and will not seek permission for any future search at our home.”