Mourners and officers stood side by side as the funeral procession set off from Westminster towards Southwark Cathedral.
Thousands of police officers representing every force in England and Wales have also turned out to say a final farewell to their colleague.
In attendance will also be 50 members of PC Palmer's family, including his parents and his young daughter.
Yesterday, the officer's coffin was draped in the flag of the Metropolitan Police as it was taken to a chapel just a short distance from where he died.
PC Palmer, 48, rested at St Mary Undercroft in the Palace of Westminster for 24 hours ahead of his funeral today.
The special distinction of a “lying-instate,” normally reserved for senior royals and politicians – went ahead after the Queen gave her consent.
Police officers protect floral tributes left ahead of PC Palmer's funeral
During the service, PC Palmer’s coffin will be received by the Dean of Southwark, The Very Reverend Andrew Nunn, who will also welcome the congregation.
Prayers will be taken by Reverend Prebendary Jonathan Osborne, Senior Chaplain to the Metropolitan Police Service.
Chief Inspector Neil Sawyer, who worked with PC Palmer in Bromley Borough and the Territorial Support Group, will then deliver a tribute to the fallen officer.
The service will feature a number of Hymns, including "I heard the voice of Jesus say" written by Horatius Bonar.
Officers stand guard near floral tributes left ahead of the funeral
Get Quotes on Home Insurance
Officers arrive for the funeral in London
The Commendation and Farewell will be delivered by the Right Reverend Christopher Chessun, The Bishop of Southwark.
At the conclusion of the service, a bugler from the Honourable Artillery Company will play the ‘Last Post’.
The bugler, Lance Corporal Graham Haynes of the Honourable Artillery Company, is also a serving officer within the Parliamentary and Diplomatic Protection Command.
Following this, a private committal will be held.
Floral tributes blanket the street near the site where the PC died
Officers were told to travel to London in plain clothes
Yesterday 12 police officers in full dress uniform formed a guard of honour as eight pall bearers in tail coats brought PC Palmer’s coffin to the chapel.
Four other people were innocently killed and dozens of others injured in the 82-second attack on Wednesday March 22, which ended with lone-wolf attacker Khalid Masood being shot dead.