The judge said the trial must not be further delayed. He said: "The family must have closure."
Mr McCluskie lived in Peter Street, Hackney, east London, with his 29-year-old sister.
She went missing after attending the £650 million opening of the new Royal London Hospital in Whitechapel, east London.
Her limbless body was seen floating in the water a week later.
Miss McCluskie played Kerry Skinner in the BBC soap in 2001.
The defendant joined friends who launched extensive searches across east London to find her.
Former EastEnders co-stars Natalie Cassidy and Brooke Kinsella both appealed on Twitter for help.
More top news
George Michael died in December last year at the age of 53.
PC Keith Palmer, 48, stabbed by Khalid Masood while on duty in the grounds of the Palace of Westminster last Wednesday.
Those gathered on the bridge fell silent at 2.40pm - the time the first call was made to police exactly seven days ago.