[For the third book in the Shades of London series, please see 'The Shadow Cabinet']
The Cabinet's mission in England is to protect the eight stones responsible for separating the living from the dead, and to keep the stones from being moved from where they can act their most effectively. The identity of only two of these stones is known: the Oswulf Stone, and the 12 termini, which were the original Crown Jewels before being shattered.
If a ghost touches one of these stones they are destroyed in a flash of light. No one knows if they go to an afterlife or not.
The Cabinet & Shades Edit
According to Stephen, there is always one member of the Shades who has infiltrated it as a part of the Cabinet, even after a branch of the Shades is suddenly disbanded and re-formed. In this case, that is him. Currently he is the only one who knows that it really exists, while the other characters all believe it is a conspiracy theory. He pretends to believe so as well. The Shadow Cabinet either recruited him because of his discretion, or his place as the Shades leader, or perhaps both reasons. He said that they approached him early on in his career, but it's unknown if that was before he met Boo (his first recruit) or after.
In Practice Edit
Despite their benevolent motive, the Shadow Cabinet itself does shady deeds to succeed in their mission, such as following and watching potential recruits, presumably without their knowledge, before approaching them and explaining bits and pieces to him/her. Although it's unknown what would happen if a Shade declined to join them, once he or she does, it becomes their top priority, they must keep their involvement in the Cabinet a secret, and they can't quit.
After Rory gains the power to destroy ghosts on contact, The Cabinet apparently sees her not as a person, but as a stone to be kept in London and watched over by them.
The oldest known mention of the Cabinet is in reference to Thomas Blood's attempt to steal the Crown Jewels in 1671, but it is believed to be older than that.
There are many rumors about the Shadow Cabinet online. Stephen says that the most ridiculous ones are actually created by the Cabinet itself to make it seem implausible to everyone except the aforementioned conspiracy theories. As a member himself, Stephen knows about other especially spiritual cities: Paris, Giza, Rome, Shanghai, Baghdad, New York, Santiago, New Delhi, Sao Paulo, Alexandria, New Orleans, and unnamed others. These places are believed to be more spiritually active because they are near large bodies of water, a spiritual magnet. It can also be assumed that they each have their own branches of the Cabinet.
According to Thorpe, the British government has no knowledge of the group, but it can be speculated that his higher-ups might. They intentionally share a name with a government Cabinet to cause confusion.
For some reason, the roman numerals one through twelve, with two repeating sevens, is significant to them.