Rear extension onto existing building that has a non insulated cavity wall - insulation ideas welcome

[Lars P]

Just about to start insulating a timber frame one storey rear extension. It'll get about 180mm PIR in walls and ceiling and 75mm in floor. So that's nice and warm.
But, - the existing house - from the nineties has a cavity wall with 140mm AAC on the inside (meeting building regs back then - and kind of ok) but brick on the outside. The cavity is not insulated, and during the work on the extension work it was clear there's a strong breeze going through that cavity.  So come winter I assume that will be as warm as a single skin brick wall 🥶 - and do anything it can to cool down the extension. Any ideas on how to insulate that outside - but now inside - brick wall - or how to close the cavity behind it to stop the breeze ? 
Thank you so much