Demonstrators threw custard and apple crumble at a display case containing the Crown Jewels.
Police were called shortly before 10:00 GMT on Saturday after four protesters defaced the case containing the Imperial State Crown, before two protesters left the scene.
The Met said in a statement that four people had been arrested on suspicion of criminal damage and taken into custody.
The Tower’s Jewel House has been closed to the public while the police investigation continues, the force said.
Take Back Power, which describes itself as a new non-violent civil-resistance group, claimed it was behind the act.
The group said it carried out the stunt to demand the UK government establish a permanent citizens’ assembly – a “House of the People” – with the power to “tax extreme wealth and fix Britain”.
The Met Police tell us: “Officers worked closely with City of London Police and security officers and four people have been arrested on suspicion of criminal damage. They have taken into custody.
“The Jewel House has been closed to the public while the police investigation continues.”
