The Met Police said members of the crowd threw missiles at officers and breached police lines in Princes Gate, Knightsbridge, on Sunday afternoon.
It comes as protests in Iran spread across the world, sparked by the death of Mahsa Amini in custody after being detained by Iranian morality police.
At least five officers were seriously injured, the Met Police said.
Twelve people have been arrested on suspicion of violent disorder offences.
Dozens of protesters in London chanted "death to the Islamic Republic" and were seen waving Iran's pre-revolutionary national flag.
Comment: Why are some of these protesters being aggressive to British police? The UK has done everything in its power, in league with the US and Israel, to try to destroy Iran.
London mayor Sadiq Khan described the scenes as "completely unacceptable".
"The selfish minority who attempted to hijack a peaceful protest must be brought to justice," he said.
Footage posted online from Sunday's protest showed scuffles breaking out among those in the crowd.
One clip showed two officers wrestling a campaigner - who appeared to have broken through the police line - to the ground.
Image source, ReutersImage caption, Angry protesters shouted on the streets of central London while making their way to the Iranian Embassy near Hyde Park
Elsewhere, riot police could be seen trying to clear protesters off the road near Marble Arch.
The Met said the demonstrators had moved from the embassy towards Marble Arch and then to Maida Vale where the Islamic Centre of England was targeted.
Masonry, bottles and other projectiles were thrown and a number of officers were injured, the Met said. At least five people ended up in hospital with injuries including broken bones.
Police believed those taking part in the protest showed "substantial group intent on causing disorder".
In Iran, officials say 35 people have been killed since protests broke out over the death of Ms Amini. Clashes continue in several cities.
She was detained after being accused of violating the law requiring women to cover their hair with a hijab and their arms and legs with loose clothing.
There are reports that officers beat Ms Amini's head with a baton and banged her head against one of their vehicles.
The police have denied that she was mistreated and said she suffered "sudden heart failure". But her family has said the 22-year-old was fit and healthy.
Comment: Apparently 'Sudden Adult Death Syndrome' (aka death by experimental covid vaccine) is only applicable to world class athletes. See the link below for alleged footage of Ms Amini's collapse whilst in custody.
Protests have taken place around the world in countries including Poland, Canada, Chile and Iraq.
Comment: Below is some footage from the protests, some media from Iran and the protests that have occurred in favor of the government, along with some balanced commentary - see also: Iranian police claim woman arrested over hijab died of heart attack in custody - incident sparked protests