Officers were called to concerns for the welfare of the 61-year-old occupant of a housing block in Mayes Road, Wood Green.
He and his daughter, 31, were unresponsive by the time paramedics arrived at the property about 9.30am on Sunday.
A 52-year-old man was arrested on suspicion of murder at an address 70 miles away in Huntingdon, Cambridgeshire. He was known to them and remains in custody.
Cambridgeshire officers were alerted to reports of a man acting suspiciously.
While engaging with police, the man made comments which prompted a request for the Met to visit Mayes Road where they discovered the two with stab wounds.
Scotland Yard said: “Formal identification has yet to take place but we believe they were father and daughter.”
Neighbours in the block of flats, which is on top of a shopping centre, said they had spotted an older man and a couple living there.
They also said that the police had visited the property several times before.
A 59-year-old man living opposite told The Times: “I was at home lying on my bed and heard people speaking outside. There were about ten or more officers knocking on doors.
“They asked me if I heard anything yesterday but I was out.”
He added that a man who lived in the flat did not speak to locals and his daughter was thought to be living with him.
Detective Chief Inspector Claire Hine said: “This incident has taken the lives of a father and daughter.
“Our thoughts are with their loved ones as they come to terms with such an unimaginable loss. We are providing and will continue to provide them with whatever support we can.
“We believe that the victims and the man in custody were known to each other and while the investigation is still in its early stages, I am confident that we are not looking for additional suspects and that there is no continuing risk to members of the public in the area.
“I would ask anyone who heard anything unusual or witnessed any suspicious behaviour in the vicinity of Mayes Road, either this weekend or at another time, to contact the police.
“Information that helps us to build a picture of what has taken place in this case could be very important.”
Anyone with any information should call 101 quoting the reference 2183/28NOV or call Crimestoppers anonymously on 0800 555 111.