Masood killed three other people, before he was shot by police. Last night a further 17 people remained in hospital, including one with life-threatening injuries.
Palmer's Auckland-based family declined to comment yesterday with a spokesperson saying they "were trying to keep out of it and didn't want to say anything."
It is understood the family were in the UK a few years ago for a family reunion.
Palmer, who was 48 and joined the police in November 2001, was married and had a 5-year-old daughter.
A fundraising page, set up to support Palmer's relatives, has raised nearly £600,000 ($1.06 million).
In a statement released by the Metropolitan Police, Palmer's UK-based family said he would be missed.
"Keith will be remembered as a wonderful dad and husband. A loving son, brother and uncle. A long-time supporter of Charlton FC.
"Dedicated to his job and proud to be a police officer, brave and courageous.
"A friend to everyone who knew him."
Tributes for the fallen police officer include heartfelt comments from British Prime Minister Theresa May who said "he was every inch a hero".
One of his policing colleagues, PC James Aitkenhead, described Palmer as "a genuinely nice person".
"Nobody had a bad word to say about him," he told British media.
"When I heard what had happened I knew it would be him because that's just the sort of guy he was, to step straight in when others might step back.
"He was always so positive, always staying late after everyone else and getting in early."
Palmer had served in the police force for 15 years and was a proud member of the Metropolitan Police's parliamentary and diplomatic protection command.
Two years ago he was nominated for the 'best thief taker' in the Commissioner's Excellence Awards, having made more than 150 arrests in 12 months.
