Chair Lady Justice Thirlwall yesterday revealed she was sent the plea last month from counsel for the management team at the Countess of Chester.
She also said she received a written request from Letby's new solicitors asking for her to pause the probe.
It came weeks after an international panel of neonatologists and paediatric specialists claimed bad medical care and natural causes were the real reasons for baby collapses and deaths on the neonatal unit.
Those medical findings have been passed to the Criminal Cases Review Commission, which investigates potential miscarriages of justice, and Letby's legal team hope her case will be referred back to the Court of Appeal.
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The application by the legal team on behalf of former Countess of Chester chief executive Tony Chambers, medical director Ian Harvey, director of nursing Alison Kelly and HR director Sue Hodkinson is expected to argue that there is a real chance that the killer nurse's convictions will be overturned.
Lawyers will submit that continuing the inquiry without considering the potential of Letby’s innocence being reviewed by the CCRC would be a breach of the duty to act fairly under the Inquiries Act.
But barristers representing the families of the dead babies are expected to hit back, suggesting the managers are trying to absolve themselves of blame.
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Letby’s own solicitors are said to have warned Lady Justice Thirlwall her final report would “not only be redundant but likely unreliable” if it was not put on hold until the CCRC ruling.
Their letter reportedly said: "It is es...