Man cut throat of daughter, three.
The former teacher, 50, arrived in England after his wife and children fled here from him in Portugal.
But the woman, 38, was arrested on false allegations of assault he made against her.
When she was in custody, the man cut his three-year-old daughter's throat and tried to strangle his son at their home in north London.
Sentencing him at the Old Bailey to life with a minimum term of 23 years for murder, Judge Martin Stephens said: "This unspeakably evil case was from your desire to control your family. You believed another man might enter the lives of your wife and children."
The man admitted murder and attempted murder. He was given a concurrent 12 years for the second offence.
The family cannot be identified to protect the surviving child, aged nine, who escaped death by running away.
Crispin Aylett, prosecuting, said the woman was arrested after her husband told police she had punched him.
Next day, the boy ran out of the house after his father placed cables on both children's necks. He pleaded with neighbours: "Help, help me, my father is trying to kill me and trying to kill my sister. I think she has already died by now."
The mother told the court in a statement: "I came to this country looking for peace and quiet and for the wellbeing of my children."