Arthur Simpson-Kent, 48, appeared at an extradition hearing in Accra.
He said he voluntarily submitted and would have returned to the UK previously had he not been arrested.
He left the UK on 19 December following the deaths of his former partner Ms Blake, 43, and their two young sons, Zachary, eight, and four year-old Amon.
During the hearing he told the court he had not travelled to Ghana to run away and was not fleeing justice.
He was arrested at a Ghanaian beach resort on 9 January.
Ms Blake, who had motor neurone disease, and her sons died from neck and head injuries, post-mortem tests found.
She played Frankie Pierre in 56 episodes of EastEnders between 1996 and 1997.
The Metropolitan Police launched a murder investigation after Ms Blake, who was last seen in public on 13 December, was found buried in the garden of the family home in Erith, with the two children, on 5 January.
The Met has been criticised over delays in its investigation which the police watchdog, the Independent Police Complaints Commission, is investigating.
The partner of an ex-EastEnders actress who was found dead with her two sons in a London garden, has told a Ghanaian court he will return to the UK.