Palmer was fatally stabbed by Khalid Masood who had ploughed a rented car into pedestrians, killing five in total before he was shot dead.
Hundreds of uniformed officers lined the cortege route from a chapel at the parliament building where Palmer's body had lain overnight to Southwark Cathedral beside the River Thames.
A floral tribute on the hearse to the 48-year-old who was married with a daughter simply read: "No. 1 Daddy."
Among mourners at the cathedral was new London police chief Cressida Dick, on her first day in the role.
Sara Thornton, head of the National Police Chiefs' Council, told reporters: "I don't think we will have ever seen a police funeral of this size..."
Palmer had not hesitated to act when confronted by a terrorist, she said.
"His bravery and his courage are something that all officers are very proud of," she added, "but also there is a tremendous sense of sadness and of loss."
Palmer's name was also added to the National Police Memorial, which records the names of those killed in the line of duty, during a ceremony in London.
Enter a name and e-mail address and we will e-mail this website link too them.