The Extinction Rebellion demonstrators parked an old fire engine outside the 100-year-old building with 1,800 litres of coloured water on board.
But they quickly lost control of the hose and the red liquid was instead sprayed across the road.
Five men and three women, aged between 34 and 83, have been arrested on suspicion of criminal damage.
Protesters say they are “highlighting the inconsistency between the UK government’s insistence that the UK is a world leader in tackling climate breakdown and the vast sums it pours into fossil fuel exploration and carbon-intensive projects”.
Phil Kingston, an 83-year-old activist, said: “I fight with all my being for my four grandchildren in this situation of existential danger.”
A Metropolitan Police spokesman said there were no reported injuries and the fire engine had been seized and removed from the scene.