OK. I think we are getting a little carried away here.
The Circle of Creation, a.k.a The Sanctuary, is modelled on Westminster Abbey...
The Consilium holds its meetings in the NAVE and more commonly in the space used for the Choir and Sanctuary (before the alter) - so the area roughly in the middle between the transepts.
The Adamantine Arrow has its 'offices' or space at the west end of the cathedral and extending into the towers there.
The Guardians of the Veil have 'offices' and space in the buildings attached at the western end of the Cloister / Common Yard.
The Silver Ladder has space in what would be the South Transcept (the area immediately south of where the Consilium usually gathers for meetings). That Order's 'offices' extend into a space labelled "Conclaves" on the maps provided in the wiki, which in RL maps of Westminster Abbey is the old Chapter House.
The Mysterium has space in some buildings attached to the southern end of the Cloister / Common Yard that extend to some underground areas in which the 'Athenaeum" is located.
The Free Council 'offices' cover a number of small side chapels at the eastern end of the building, including the impressive Henry VII chapel - and I suspect this is where the confusion lies. The area marked "Assembly Hall" is the Henry VII chapel - and that space is reserved for an actual FC Assembly, should one ever meet.
It is not where the Consilium meets. It would be nice if it did, but it doesn't*.
The main building of the abbey (and by extension, of the Circle) is a big, vaulted, echoing, and largely empty space. Not many internal walls but lots of pillars supporting the roof. For reference, only the little chapels up at the FC end of the building are enclosed and those enclosures don't have doors (not even the Henry VII chapel although it certainly feels like it does).
*I have visited Westminster Abbey a couple of times. Henry VII chapel is one of my personal favourites as it has banners, fan vaulting in the ceiling, and choir stalls that make it look like a senate chamber or something (kind of why it is labeled as 'Assembly Hall' for the FC.)