Extinction Rebellion campaigners parked a pink boat at Oxford Circus and blocked Marble Arch, Piccadilly Circus and roads around Parliament Square.
Protester Yen Chit Chong said: "This is our last best shot at survival."Among a total of 52 arrests, five people were detained on suspicion of criminal damage at Shell's HQ.
The three men and two women were taken to a police station in central London after a glass door was smashed at the offices near Waterloo.
The majority of those arrested were detained on suspicion of public order offences.
Just after midnight on Monday, Transport for London (TfL) confirmed it had suspended bus services on the N18 route because Great Portland Street was blocked by protesters.
Earlier, police had ordered the protesters to restrict their actions to the Marble Arch area to prevent further disruption.
Organisers claim protests have been held in more than 80 cities across 33 countries.Protester Olivia Evershed, 23, said: "I hope that it's really going to bring awareness about the emergency crisis that we are in, and encourage the government to act.
"We've got 12 years to act before there is irreversible damage to the environment and we start to see catastrophic changes. If we don't do anything to change this, our children will die."
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, protesters unfurled banners, held up placards and waved flags as speakers took to the stage.
Who are Extinction Rebellion?
Since its launch last year, members have shut bridges, poured buckets of fake blood outside Downing Street, blockaded the BBC and stripped semi-naked in Parliament.
It has three core demands: for the government to "tell the truth about climate change", reduce carbon emissions to zero by 2025, and create a citizens' assembly to oversee progress.
Controversially, the group is trying to get as many people arrested as possible.
One of the group's founders, Roger Hallam, believes that mass participation and civil disobedience maximise the chances of social change.
But critics say they cause unnecessary disruption and waste police time when forces are already overstretched.
By intentionally causing more than £6,000 damage at the Shell headquarters activists aim to get the case into crown court to put their case to a jury, the campaign said.
A Shell spokesman said: "We respect the right of everyone to express their point of view. We only ask that they do so with their safety and the safety of others in mind."
Protester 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 Department for Business, Energy & Industrial Strategy by chaining themselves together on the pavement, leading to 85 arrests.
At the scene
By Matthew Cannon, BBC News
The unusual sight of a pink yacht stands in the centre of Oxford Circus, surrounded by protesters holding aloft a sea of coloured flags.
The focus here is on the future of the planet - and there is a sense of urgency.
Some are wearing red to symbolise "the blood of dying species", one group wants to "save the bees", while a man dressed as a centaur holds a placard which says "climate change is not a myth... unlike centaurs".
Two young women tell me they are not willing to have children due to their fears for the world they will be bringing them into.
Another man, who plans to protest through the night, says the protests will be peaceful but he is willing to be arrested.
"The more the authorities will get fed up with us the more it brings us to their attention," he said.
Organisers have encouraged people to set up camp in Hyde Park overnight into Tuesday - 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 was not allowed.