The incident, which occurred on 20 June, reportedly involved members of Palestine Action and caused approximately £7 million worth of damage.
Amy Gardiner-Gibson, Jony Cink, Daniel Jeronymides-Norie, and Lewis Chiaramello were charged with conspiracy to enter a prohibited place and conspiracy to commit criminal damage.
The defendants appeared at Westminster Magistrates’ Court and are scheduled to appear next at the Old Bailey on 18 July.
Counter Terrorism Policing South East is investigating the incident, with a 41-year-old woman released on bail and a 23-year-old man released without charge.