Members of campaign group Extinction Rebellion have also parked a boat at Oxford Circus, and blocked Marble Arch as part of a global day of action.
Yen Chit Chong, from Extinction Rebellion in London, said: "This is our last best shot at survival."
Police have advised people travelling into London to allow extra journey time. No arrests have been made.
Extinction Rebellion said protests would continue throughout the week "escalating the creative disruption across the capital day by day".
The group said it planned to "bring London to a standstill for up to two weeks", and wanted the government to take urgent action to tackle climate change.
In Parliament Square, others unfurled banners, held up placards and waved flags as speakers took to the stage.
Protestor Chay Harwood told the BBC: "We live in a very sick society at the moment there's a lot of social issues and social ills that need curing.
"But at the moment the biggest threat we face is the threat of climate change."
The Met said it had "appropriate policing plans" in place for the demonstrations and officers from across the force would be used "to support the public order operation".
In November, activists blockaded the UK's energy department by chaining themselves together on the pavement, leading to 85 arrests.
Organisers were encouraging people to set up camp in Hyde Park overnight into Monday - an offence under Royal Parks legislation.
A spokeswoman for The Royal Parks said Extinction Rebellion had not asked for permission to begin the protest in the park and that camping is not allowed.
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