A breather membrane can/should only be used where there is a ventilated cavity so that it can actually allow evaporation. If it is pressed up against a wall it will stay wet, allow water to pass through it the wrong way and not permit moisture to pass through it the right way either.
Lots of people misunderstand the concepts behind what needs to breathe and what does not. Not all timber walls need to breathe. You are not constructing a timber frame so what you are doing there does not need to breathe - if it did you need a ventilated cavity.
What you should be doing there is preventing moisture from coming in through the wall from the outside and into the wall from the inside, and then that timber stud wall does not need to breathe or be ventilated. So you put an impermeable layer, not permeable layer, on the back of the brick wall, and another on the front of the timber wall.
And for this to work, you need to ensure that there are no air voids within the wall, so it needs to be filled with insulation.