The buildings, including the headquarters of the Secret Intelligence Service, were targeted using fire extinguishers loaded with orange paint about 8.30am on Monday.
The group said the buildings were chosen to represent “the four pillars that support and maintain the power of the fossil fuel economy — government, security, finance and media”.
The Metropolitan Police said six people have been arrested on suspicion of criminal damage and taken into custody at a central London police station.
City of London Police officers arrested a further two people who sprayed the Bank of England.
A Just Stop Oil spokesperson said: “We are not prepared to stand by and watch while everything we love is destroyed, while vulnerable people go hungry and fossil fuel companies and the rich profit from our misery.
“We are acting to stop new oil and gas because it is the right thing to do. As citizens, as parents we have every right under British law to protect ourselves and those we love. The government has the power to end the disruption today by agreeing to stop new oil and gas licences and consents.”
Supporters are calling on the Government to end all new oil and gas projects by 2025.
Monday’s stunt follows four weeks of disruptive protests by supporters, during which the police have made 637 arrests, the group said.
A High Court judge has ordered more than 180 named Just Stop Oil protesters not to block roads in London.
Mr Justice Freedman granted an injunction at a High Court hearing in London on Monday after an application by Transport for London.
Another judge had recently made an order against 62 named people.
Mr Justice Freedman continued that injunction and ruled that an order should also be made against a further 121 named people.
Many protests involve spray painting prominent Government and commercial buildings, and people gluing themselves to busy roads or famous paintings in galleries.
Londoners have been warned by the Met not to “directly intervene” with disruptive Just Stop Oil protesters.
Assistant Commissioner Matt Twist urged people not to take the law into their own hands after activists blocking roads in London were dragged out of the way in heated scenes on Saturday.
The environmental campaigners caused huge build-ups of traffic on Saturday afternoon by sitting in the middle of streets including Kensington High Street, Charing Cross Road, Kennington Park Road and Black Friars Road.