Pavinya (left) and Nigish both died in the attack by their father
Nadarajah Nithiyakumar, 41, attacked his daughter, 19-month-old Pavinya, and son Nigish, who was three, while their mum was in the shower on Sunday, 26 April.
She discovered what had happened and alerted emergency services.
Police and paramedics rushed to their home in Aldborough Road North but Pavinya was pronounced dead and Nigish passed away in hospital.
Nithiyakumar has appeared today at the Old Bailey, where he pleaded guilty to manslaughter by diminished responsibility.
That was accepted by prosecutors and he has been remanded at a mental health centre ahead of sentencing on Thursday, 10 December.
For more on this story, and the latest on our other local and national news, listen to Time 107.5FM