The new hearing will be at St Pancras Coroner's Court on Tuesday January 8.
Suzanne Greenaway recorded a verdict of misadventure at the original hearing last year.
She was chosen for the role in July 2009 by her husband, Andrew Reid, who was the coroner for Inner North London, after she had worked as a solicitor and barrister in Australia.
But she stepped down in November when it emerged she did not have the required five years' experience in the Law Society.
Dr Reid resigned from his position this month after the Office for Judicial Complaints (OJC) launched disciplinary proceedings against him.
Investigators found he had not "thoroughly" checked his wife had the requisite qualifications for the position.
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The results of the first preference votes counted so far gives an early indication that Mr Khan is line to take power at City Hall.
Mr Goldsmith's campaign, run by Sir Lynton's communications firm has come under fire from Labour.