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
The former pub chef who brutally raped and murdered teenage model Sally Anne Bowman has admitted raping another woman.
Ministers outlined proposals to ban the sale of new petrol and diesel vehicles from 2049 as part of a new clean air strategy.
His famous 2002 picture on the wall of a Shoreditch shop, Balloon Girl, came top of a list of British art.