The funeral service was led by the Dean of Southwark The Very Reverend Andrew Nunn and is being followed by a private cremation.
The Met's senior chaplain, the Reverend Prebendary Jonathan Osborne, led the prayers and Chief Insp Neil Sawyer, who worked with PC Palmer in Bromley and the Territorial Support Group, paid warm tribute to his colleague.
Hymns including I Heard The Voice Of Jesus Say were followed by a rendition of The Last Post by a bugler from the Honourable Artillery Company.
Officers bowed their heads as the Last Post sounded from the cathedral shortly after a recital of the Lord's Prayer.
A few moments' silence then followed a rendition of God Save The Queen, as on-duty officers, medical staff and members of the public stood still in respect for PC Palmer.
Around 50 members of PC Palmer's family including his wife, child, mother and father, brother and sisters are attended the service.
A floral tribute left on top of the hearse read: "No 1 daddy".
The cortege was led by the Metropolitan Police Colour Party and a "Black Guard" of mounted officers.
PC Palmer's coffin travelled 2.6 miles along some of the capital's usually bustling streets – but avoiding the scene of last month's atrocity on Westminster Bridge – to arrive for the 2pm ceremony.
Police officers protect floral tributes left ahead of PC Palmer's funeral The funeral of PC Keith Palmer in pictures Mon, April 10, 2017
The funeral of the police officer who lost his life in the Westminster terror attack is scheduled for today at 2pm. His body was transferred to the Palace of Westminster yesterday, where a private memorial service was held for members of his close family
EPA 1 of 23
Police officials and mounted police lead the hearse carrying the coffin of London Metropolitan Police Officer PC Keith Palmer during his funeral parade
Thousands of police officers representing every force in England and Wales turned out to say a final farewell to their colleague.
Get Quotes on Home Insurance
Met commissioner Cressida Dick – the first female head of Scotland Yard in its 188-year history – also attended the funeral.
It was her first public engagement in her new role.
PC Palmer’s coffin was received by thet he Very Reverend Nunn, who also welcomed the congregation.
The officer's name has been added to the police roll of honour at the National Police Memorial in London.
Floral tributes blanket the street near the site where the PC died
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.
Twelve 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.
Officers were told to travel to London in plain clothes
A Metropolitan Police flag flies from Southwark Cathedral