Hairdresser Arthur Simpson-Kent, 48, is charged with murdering his 43-year-old girlfriend and their sons Zachary, eight, and four-year-old Amon between December 12 and December 16 last year.
The victims vanished on December 13 and their bodies were found buried in the garden of the family home in Erith, Kent, on January 5.
The following month, Simpson-Kent was arrested at Heathrow Airport after agreeing to his extradition from Ghana.
Simpson-Kent appeared via video link from Belmarsh prison before Mr Justice Singh at the Old Bailey.
Dressed in a red T-shirt and dark trousers, the bearded defendant spoke only to confirm his name.
He was to due enter pleas to the charges ahead of a provisional trial fixed for October 4.
However, arraignment was put off and the senior judge set a new timetable for the case.
Defence lawyer Jim Sturman QC told the court that his client had admitted the killings.
He said he had no objection to the defendant's position being reported.
The defendant was remanded in custody until his next hearing on July 29 when he is expected to enter pleas.
Mr Justice Singh confirmed he would be the trial judge.
Ms Blake played Frankie Pierre in 56 episodes of EastEnders between 1996 and 1997. She was suffering from motor neurone disease before she died.
At the time of her disappearance, her family said they were using their faith in Christ to get them through.
"We've got to use our faith to get us through this," her sister Ava said.