Thousands of police officers lined the route of a 2.6-mile funeral cortege starting at the Palace of Westminster.
PC Palmer, 48, who was married with a five-year-old daughter, was guarding the Houses of Parliament on 22 March when he was stabbed by Khalid Masood.
A floral tribute left on top of his hearse read: “No 1 daddy”.
The service, which is being attended by around 50 members of PC Palmer’s family including his wife, child, parents, brother and sisters, will be followed a private cremation.
Officers and members of the public lined the route as his coffin travelled from a chapel at the Palace of Westminster.
His body had been lying in rest there by special permission of the Queen.
The Charlton Athletic season-ticket holder had served in the Metropolitan Police for 15 years.
Members of his family attended a short private service in the chapel on Sunday, before officers watched over his coffin throughout the night.
Two thousand Met officers are on duty for the funeral in policing and ceremonial roles.
Sara Thornton, who leads the National Police Chiefs’ Council, said officers from all over the country were travelling to London to line the route, while others were holding a two-minute silence outside police stations as the funeral takes place.
‘Sadness and loss’
“I don’t think we will have ever seen a police funeral of this size,” she said.
“Keith didn’t hesitate to act when confronted by a terrorist – his bravery and his courage are something that all officers are very proud of, but also there is a tremendous sense of sadness and of loss.”
Special sergeant Matthew Warden, from Nottinghamshire, made the journey “because we are all one big family” and special constable Amanda Stansfield, from West Yorkshire Police, said she wanted to show support for her London colleagues.
“I just sat and cried when I heard the news,” he added.
Another well-wisher, David Lewis, from Orpington, said it was important for ordinary Londoners to pay their respects.
“It just shows as a country that we want to pay our respects to somebody that gave their life to protect the rest of us,” he said.
The Very Reverend Andrew Nunn, the dean of Southwark Cathedral, told the BBC that it was vital both that the family could grieve privately and for the public to pay their respects.
“I hope for the family they receive the comfort that they need through the service, because they’re having to grieve publically and that must be a very, very difficult thing,” he said.
“But then the rest of the nation needs to pay its respects and say thank you for what PC Palmer actually did in defending in the place where he was serving.”
PC Palmer’s name was also added to the National Police Memorial, which records the names of officers who have been killed in the line of duty, during a special ceremony in London.
The funeral is the first engagement for new Metropolitan Police Commissioner Cressida Dick.
Flags were flying at half mast above New Scotland Yard to honour PC Palmer.
Before attacking PC Palmer, Masood had driven his car into crowds on Westminster Bridge, causing injuries that have resulted in four deaths.
Romanian Andreea Cristea, 31, who fell from the bridge into the River Thames, died in hospital on Thursday.
Aysha Frade, 44, who worked at a London sixth-form college, US tourist Kurt Cochran, 54, and retired south London window cleaner Leslie Rhodes, 75, were also killed.
Masood was shot by police officers in New Palace Yard, inside the Westminster estate, after he had fatally stabbed PC Palmer.