A group of women used hammers to crack the windows before staging a sitdown protest at around 7am on Thursday.
Nine people have been arrested on suspicion of criminal damage, the Metropolitan Police said.
The activists wore patches stating “better broken windows than broken promises”, in reference to the suffragettes.
In a statement on Twitter the group said: "HSBC is Europe’s second-largest financier of fossil fuels and has funded £81 billion to #fossilfuel since 2015 #ParisAgreement
"These companies are killing us."
London mayoral candidate Valerie Brown, 68, was among the activists who broke the windows.
In a statement provided by the group she said: “Investing in fossil fuels is murder. More and more people can see that clearly. Why can’t you?”
She added: “We will not stand by whilst you invest in runaway greed, whilst people’s lives are being shattered by the fossil fuel industries.”
A spokesperson for HSBC said the bank cannot condone vandalism.
““We welcome meaningful dialogue on our climate strategy, however, we cannot condone vandalism or actions that put people and property at risk”, they said.
“We have an ambition to be net-zero by 2030 and to bring our financed emissions to net-zero by 2050.
“We have also committed to set out short and medium-term transition targets, and to phase out the financing of coal-fired power and thermal coal mining by 2040 globally. We remain committed to supporting our customers in their transition to net-zero.”
It follows a similar incident last month when seven protesters from the group used hammers and chisels to break windows at Barclays in Canary Wharf.
The women put stickers on the glass that read “In case of climate emergency break glass”, before damaging the windows at around 7am on Wednesday.
They then sat down and waited to be arrested.