Half Brick, Half wooden Frame wall

[Spoonhead12]

I noticed in the bedroom dormer in my house that the wall under the window is very cold. I decided to open up a small hole in the plasterboard to check it out. Turns out there was a hole to the outside and a bird had made a nest in the wall.

Once I fix that, I want to insulate the wall, so i opened the whole a bit bigger just so I could get an idea of the type of wall I was dealing with, and it's not what I was expecting, basically from the floor to halfway up the wall it's a brick cavity wall. On top of the brick cavity wall from the halfway point to under the window is a wood frame.

I'm not sure the best way forward, should I:

Fill the wooden frame with insulation but leave the brick with non and then put plasterboard back up

Or

Get plasterboard that has insulation attached and then fix it t the wall with screws for the wooden frame half and glue/dot and dash for the brick half?

 

[noseall]

Yes, fill the timber cavities with PIR insulation then foil tape all the joints.
A second continuous layer across the brick/stud walling is a good idea and yes, this can be combined - dabbed and screwed, depending where the boards land. You may have to add slim battens to the timber frame in order to deal with the thickness of dab. Make sure you buy the dabb-able insulated boards otherwise you may need to use foam if you decide to use foil sandwich PIR.