Members of Extinction Rebellion, who are demanding urgent action to tackle climate change, also said they staged a protest in the financial district of Canary Wharf by standing on top of trains on the Docklands Light Railway.
"Many of the most environmentally destructive companies in the world have their stock market listings at the London Stock Exchange (LSE)," the group said in a statement.
"This institution literally trades in the devastation of our planet."
Seven protesters could be seen at the building's entrance, as police attempted to separate them. Trading opened as normal on Thursday.
More than 100 arrested at London climate protests
It is the latest stunt by the group which had just declared the end of an 11-day campaign of disruption across London, which at points blocked high profile locations including Oxford Street, Parliament Square, Waterloo Bridge.
More than 1,000 people have been arrested over the action and dozens have been charged.
Extinction Rebellion wants Britain's government to declare a climate and ecological emergency, act to halt biodiversity loss and reduce greenhouse gas emissions to net zero by 2025.
Their tactics of sitting down in the middle of busy roads and refusing -- peacefully -- to move have proved remarkably effective, with police struggling to remove them.
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