The protests were organised by the campaign group Extinction Rebellion, which was established last year in Britain by academics and has become one of the world's fastest-growing environmental movements.
London's Metropolitan Police said that by Tuesday evening, 290 arrests had been made.
"We expect demonstrations to continue throughout the coming weeks," the police statement said.
Campaigners daubed graffiti and smashed a window at the Shell Centre building.
The majority arrested were seized for breaching public order laws and obstructing a highway.
The protest saw more than a thousand people block off central London's Waterloo Bridge and lay trees in pots along its length. Later, people set up camps in Hyde Park in preparation for further demonstrations throughout the week.
The police have ordered the protesters to confine themselves to a zone within Marble Arch, a space at the junction of Hyde Park, the Oxford Street main shopping thoroughfare and the Park Lane street of plush hotels.
"We so far have 55 bus routes closed and 500,000 people affected as a result," the police said.
"Targeting public transport in this way would only damage the cause of all of us who want to tackle climate change," he said in a statement.
Campaigners want governments to declare a climate and ecological emergency, reduce greenhouse gas emissions to zero by 2025, halt biodiversity loss and be led by new "citizens' assemblies on climate and ecological justice".
Protesters attached themselves to vehicles and to each other using bicycle locks, said the spokesman.
"We have no intention of leaving until the government listens to us," he said.
"Many of us are willing to sacrifice our liberty for the cause.