Ms Dick, who is the first female head of Scotland Yard in its 188-year history, paid tribute to PC Palmer, who was killed in the Westminster terror attack, as she attended his funeral at Southwark Cathedral on her first day in the new role.
PC Palmer's funeral took place today at the cathedral following a procession through the streets of London led by the Metropolitan Police Colour party and a “Black Guard” of mounted officers.
More than 5,000 police officers lined the route of his funeral cortege from the Palace of Westminster to the cathedral where a private ceremony took place.
PC Palmer died in the Westminster terror attack, on March 22 while on duty at the Carriage Gates near the Houses of Parliament.
Paying tribute to the slain officer outside the cathedral after the private ceremony, she told reporters: “He was genuinely a friendly face of British policing and in this horrible, horrible sad time I think all of us in policing hope that today’s tribute to him gives some small comfort to his family.
“We can’t possibly imagine what they have been going through. We are incredibly proud of him and we know they are too and all our hearts are with them.”
During the service, Ms Dick read the WH Auden poem Funeral Blues, which begins “Stop all the clocks, cut off the telephone” and ask for “the traffic police to wear black cotton gloves” in mourning of a loved one.
Ms Dick added: “It [the poem] was chosen by the family. It was the poem that they wanted to be read. For me, it was an enormous privilege to be asked to read it.
“I think the events at Westminster have appalled the whole nation and since then I know that Met colleagues and colleagues across England and Wales have been overwhelmed by the strength of feeling from members of the public.
“It’s just wonderful to see the numbers that have turned out. It means a very great deal to my colleagues in the Met and across the country. If we take some inspiration and positivity forward from this then that is something.
“Today was about Keith, for Keith and for his family. It was a chance to honour him and his service.”
Hundreds of officers from police forces all over the country arrived on coaches in Southwark hours before the funeral which is thought to be the largest ever gathering of officers in Britain.
Rows of uniformed officers, many with service medals pinned to their jackets and wearing white gloves, marched towards the cathedral and lined the funeral route as on-duty colleagues involved in the security operation stood guard.
Boats from the Marine Policing Unit led river emergency services and lifeboats in a ten-second horn salute.
The boats formed an arrow shape as NPAS helicopters flying above created the ‘missing man formation’ salute – commonly done at funerals and memorials.
Well-wishers lined the barriers along the cortège route with between 40,000 to 50,000 members of the public expected to turn out to pay their respects.
Four other innocent people were killed and dozens of others injured in the 82-second atrocity in Westminster, which ended with attacker Khalid Masood, 52, being shot dead.
Andreea Cristea, 31, Leslie Rhodes, 75, Kurt Cochran, 54, and Aysha Frade, 44, died after Masood ploughed into pedestrians on Westminster Bridge.