"meetings of the Cabinet Council were held in the Palace"

Presumably the Cabinet Council is the equivalent in Lyra's world to the British Parliament in our own. In which case, the Palace she is referring to may be the Palace of Westminster, seat of Parliament.


The Palace of Westminster
Creative Commons Attribution Share AlikeThe Palace of Westminster - Credit: David Iliff

However, in Lyra's world the King is directly involved in politics, attending meetings of the Cabinet Council in person.  This might suggest that the Palace in question is Buckingham Palace.