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
CCTV and images show man suspected of trying to set the north London mosque alight in alleged Islamophobic hate crime
Detectives investigating a man's body washed up on the shores of the river have arrested a second man on suspicion of murder.
Keepers have the celebrating the arrival of the western lowland gorilla to 22-year-old mother Effie in captivity at the zoo.