The event also attracted far-right commentator Katie Hopkins, who was deported from Australia earlier this week after boasting about her intention to break quarantine rules.
During his speech from the main stage, Mr Corbyn attempted to lead the crowd in a chant telling the government to "Ping Off" - a reference to the NHS app's notifications to users to self-isolate.
A former nurse also urged her supporters to take down the names of medical staff.
Kate Shemirani, who was struck off by the Nursing and Midwifery Council last month for spreading Covid misinformation, said: “Get their names. Email them to me. With a group of lawyers, we are collecting all that. At the Nuremburg Trials the doctors and nurses stood trial and they hung. If you are a doctor or a nurse, now is the time to get off that bus... and stand with us the people."
London major Sadiq Khan described her comments as “utterly appalling”. He tweeted: “I have raised it directly with the Met Police. Our NHS staff are the heroes of this pandemic and Londoners from across this city roundly reject this hate.”
At the end of the rally, protesters marched from Trafalgar Square along Whitehall to Parliament Square.
Police said one demonstrator was arrested outside Downing Street after throwing a bottle at officers.
Commander Catherine Roper tweeted: "Violence will not be tolerated. We encourage the remaining crowd to continue their demonstration peacefully."
Similar protests were held in Belfast, Birmingham and Manchester, where hundreds of protesters chanted "shame on you" at police officers.
In Dublin around 1,500 protesters gathered outside Custom House before walking through the city holding anti-vaccine signs and chanting "freedom".
One speaker at the rally claimed the vaccine programme was "genocide", adding: "If people are coming to your door then you have to protect yourself from the needle because it's coming and they are coming for your kids. They are coming to kill you and that's the end of it."
The organisers of the "World Wide Rally for Freedom" claimed that protests would take place in more than 180 cities across the world.
They said they were protesting against continued coronavirus restrictions, mask rules, compulsory vaccinations and vaccine passports.
"Authoritarian coronavirus restrictions have damaged our lives more than any virus has, and even if the effects of the virus were more damaging, the restrictions to our freedoms would still have been unjust and unlawful," the group said.
An estimated 160,000 people took part in protests in France against new laws introducing vaccine passports and compulsory jabs for healthcare workers.
Police fired water cannons and tear gas to disperse protesters in Paris after a chair and other missiles were thrown at officers.
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