The Metropolitan Police said three men were also detained for public order offences during the demonstration.
A spokesperson said the teenage girl was “released under investigation” as the demonstration continued on Saturday afternoon.
It was one of several protests held in British cities by the UK “yellow vests”, who have appropriated the high-visibility jackets worn in demonstrations that turned violent in France.
Supporters called for a no-deal Brexit and shouted that the prime minister was a “traitor”, while demonstrating over other causes and conspiracy theories popular among the extreme right wing.
Police said around 40 protesters also rallied in Manchester, where some yellow vests were daubed with English Defence League (EDL) slogans and “No surrender”.
No arrests were made during the march, which was temporarily contained outside a branch of Greggs.
In London, a smoke bomb was set off on Downing Street before dozens of protesters ran up Whitehall and clashed with police officers.
Organiser James Goddard, who fundraises his activities online, filmed himself shouting: “If they want a war we’ll give them a war, let’s give them a f***ing war” in a live stream posted on Facebook.
The group blocked Westminster Bridge, one of several bridges blockaded by the same yellow vest demonstrators last month, before moving through parts of central London.
At one point they stopped traffic in Parliament Square after joining up with a protest against the imprisonment of separatist leaders in Cameroon.
The yellow vests later set fire to an EU flag as people shouted “spit on it!”, and tried to block Blackfriars Bridge.
As darkness fell, they were still marching around roads in central London, chanting “we want Brexit now”.
The Metropolitan Police said a route had not been organised for the protest, meaning roads were not closed.
As officers tried to move protesters out of a road near Parliament Square, they refused to comply and scuffles broke out.
Yellow vest demonstrators included family members of three boys killed by a drink-driver in London last year, who have been running a campaign to charge the culprit with murder. The man was jailed for death by dangerous driving.
The yellow vests disrupted a Court of Appeal hearing that saw his sentence reduced last month and have been protesting regularly in London.
In December, Mr Goddard and other members filmed themselves harassing pro-Remain MP Anna Soubry and calling her a traitor.
Live Facebook broadcasts have shown the yellow vests shouting verbal abuse through a megaphone at pro-Remain protesters and journalists broadcasting from outside the Palace of Westminster, with Sky’s Kay Burley singled out as a particular target.
A Tommy Robinson supporter who has spoken at the EDL founder’s rallies and attended numerous far-right marches, Mr Goddard attempts to crowdfund his activities on PayPal.
Also a vocal supporter of Donald Trump, he has previously called Islam a “political ideology that advocates your death” and claimed terror attacks are being “covered up” in Britain.
He had claimed Saturday would see “nationwide yellow vest protests” in locations including Sheffield, Manchester and Newport.
“We are going to make the political class listen to what we’re saying,” Mr Goddard added. “The democratic will of the people is being denied.”
He listed “political correctness, cultural Marxism and forced adoptions” as other values of the UK yellow vest movement.
Saturday’s protests came as hundreds of yellow vests marched in Paris and other French cities, for the first time in 2019.
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