Derek Chauvin has been charged with his murder in Minneapolis. The white police officer has been sacked from his job.
Some protesters appeared to be breaking lockdown rules, not staying 2m apart.
The protests have been held at Trafalgar Square and outside the US Embassy in Battersea.
Elsewhere in the UK, hundreds marched through Manchester city centre chanting “Black Lives Matter”.
The same chanting could be heard in London and the US, in reference to the civil rights campaign group. They also held up placards saying “racism has no place”, and “I can’t breathe” – a reference to Mr Floyd’s words during his arrest.
The Met Police said officers were present and were engaging with those in attendance.
It added that an “appropriate policing plan is in place”.
Reverend Sally Hitchiner, associate vicar at St Martin-in-the-Fields church on Trafalgar Square, said she could see hundreds gathered for the protest from her workplace.
“I’m very sympathetic to the issue but also surprised to see the strength of emotion that has gathered people together,” she said.
“Clearly they’re not following lockdown and social distancing, but I think there’s a huge amount of passion there and that’s overriding their concerns.
“It’s an issue that requires passion but at the same time there’s a huge amount of risk in what they’re doing.”
She said police appeared to be moving the crowd on from the square by early afternoon.
Protesters made their way to the embassy by marching along roads near the River Thames.
Traffic has been stopped in several places and protesters have received applause and horns were being sounded by passing cars.
A large portion of the crowd stopped under a railway bridge outside Battersea Park Station.
Four men climbed on top of a bus stop before getting down on one knee and with their right arms in salute in silence, leading the gathered crowd to do the same.
It is a stance made famous by Tommie Smith, the US sprinter who famously raised his fist in protest against racial discrimination during his gold medal ceremony at the 1968 Olympics.
American football player Colin Kaepernick caused outrage when he held the pose during the US anthem as a protest against racial injustice.
Tens of thousands of people have joined nightly protests across the US since the death, with at least 1,600 people arrested in 22 cities as some demonstrations descended into violence.
Hundreds of people marched through Peckham in south London on Saturday in protest against police brutality.
It comes as the US has been rocked by protests over the past five days, many of which turned into violence with cars and buildings set alight and riot police using tear gas and rubber bullets.