stud wall gap

[Palmtree]

Hi all, I’ve a victorian terrace with single story bathroom at the back.
The end wall is single skin brick and the other left and right walls are solid double brick.

I’m batoning the double brick walls, insulating in between.
On the single skin wall I’m building an inner stud wall, insulating in between studs.

It’s kind of a cell within a cell.

My question is, am I ok with the stud wall to brick wall ’cavity’ being left open to the ceiling void above (for airflow)?
Do I need a fire stop or to wedge rigid insulation in (adding a couple of air bricks to air the cavity that way instead)?

I’ve attached a simplified sketch.

Thanks in advance for your thoughts.

 

[^woody^]

You don't need a cavity or air flow.

Also, best to insulate between and across the stud work, and include a vapour check layer either via taping the insulation, polythene or foil plasterboard.