HOME Secretary David Blunkett is challenging an inquest ruling on a woman who died in New Hall prison, near Flockton.
Sheena Creamer, 22, was found dead while on remand for a dishonesty offence.
Mr Blunkett is questioning a law allowing inquest juries to blame prison authorities for deaths in custody.
Law Lords in London are examining his plea in a hearing expected to last four days.
Peter Mahy, solicitor for Sheena Creamer's mother Helen Sacker, said before the hearing that the case could have far-reaching consequences for inquest law.
He said concerns had been raised about the conduct of the locum doctor who examined Sheena the day before she died.
The doctor had made it clear at the inquest that he had no training in prison suicide procedures.
The Home Secretary is also challenging an inquest ruling on child killer Colin Middleton, 30, who hanged himself at Bristol Prison five years ago.
An inquest jury took the view, shared by the coroner, that there were "significant deficiencies" in the care given to Middleton.