The protest began peacefully, with several participants climbing the base of Nelson's column and chanting the slogan "one solution, revolution".
One woman on a loudspeaker warned "there may be kettling" as the procession along Whitehall began.
Members of the public inside restaurant Garfunkle's were also trapped inside the cordon.
Oxford University student Emma Janson, 18, came into the restaurant to get away from the mob with two friends.
She said: "We don't know how we're going to get out of here.
"We only came in here to get away from them and there was no where else to go.
"It's really uncomfortable to watch them throwing bottles and fireworks from outside the window.
"Hopefully by the time we leave they will be gone.
"It's pretty scary."
The police beamed a message in green letters onto a building in Parliament Square, which read: "Please observe Public Order Act restrictions. Failure to comply may result in arrest and prosecution. Officers may require you to remove facial covering. Failure to comply is an offence."
It came after members of the crowd ignited fireworks and flares in front of Westminster Abbey.
Angela Windsor, an unemployed 40-year-old, said she travelled from Wales to take part in the event.
"Nobody is protecting people - nobody cares," she said.
"I think everyone here cares enough about people to make the effort to come down and try and do something, because the officials aren't doing it."
She said anyone who tried to incite a repeat of last year's violent displays would be missing the point.
"Nobody wants a fight, we just want change," she said.
But she was forced to defend the wording of a sign she was brandishing - including the words "death to the monarchy" - when questioned about it by passers-by.
Commander BJ Harrington of the Met’s Public Order Command said: "I would like to commend my officers policing this challenging event for their professionalism and faultless co-ordination.
"I would also like to thank those participants who conducted themselves in a peaceful manner as well as Londoners and those visiting our city for their patience and tolerance.
“We facilitate hundreds of peaceful protests every year in London usually with the co-operation of the organisers. On this occasion although the organisers did not engage with police, the majority of protesters did adhere to the conditions imposed. Only a small minority chose to breach the conditions and engage in criminality.”Police imposed conditions on the march, limiting it to a three-hour period between 6pm and 9pm on a prescribed route between Trafalgar Square and Whitehall.
Last year's march saw ugly scenes as missiles and fireworks were thrown at police. Four officers and six police horses were injured.
More than 1,000 people are estimated to have taken part and there were more than 50 arrests.