Tony McCluskie, 35, said he suffered loss of control leading to her death on March 1.
She went missing after attending the opening of the new Royal London Hospital.
Her limbless body was seen floating in the water a week later.
Prosecutors are still waiting for a medical report to establish how she died.
McCluskie appeared at the Old Bailey by videolink from Belmarsh prison yesterday.
He pled not guilty to murder followed by a guilty plea to manslaughter.
A trial on the issue of murder or manslaughter will go ahead on January 14.