The family of murder victim Muriel McKay believe her remains are buried in a garden in east London, the High Court has heard.
Ms McKay was officially declared dead by a High Court judge earlier this month, 56 years after being kidnapped.
The 55-year-old was taken from her London home by Nizamodeen and his brother Arthur Hosein in December 1969.
They mistook her for Anna, the wife of media mogul Rupert Murdoch.
Ms McKay’s husband was newspaper executive Alick McKay, the deputy to newspaper mogul Rupert Murdoch.
The kidnappers realised their mistake, but still demanded a £1m ransom for her safe return.
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The two Hosein brothers were convicted and jailed for life in one of the first murder trials without a body. Arthur Hosein died in prison.
On Monday, barristers for two of Ms McKay’s children, Ian McKay and Dianne Levinson, asked a judge to order that the homeowners of two neighbouring properties on Bethnal Green Road allow the family to conduct a “ground-penetrating radar survey” of a shared back garden.
One of the homeowners, Madeleine Higson, opposes the injunction bid, which would also stop her from disturbing the garden.
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Mr Justice Richard Smith said he will hand down his judgment at 2pm on Tuesday, stating the case involved “not uncomplicated legal sensitivities”.
Speaking following the hearing, Ms McKay’s grandson Mark Dyer said the bid to discover her remains was “important to the whole family”.
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He said: “We do not want to be felt sorry for, we just actually want to get on and … scan the place, check for my grandmother.
“We’ve been told she’s there, most probably there, so we need to pick her up.
“She would like to come home for Christmas this year and what is left of her is purely some remains, some bones.
“They should find a place where the family can go and visit, where whoever’s interested in what happened to her should go and visit, and that’s the right thing to do.”
