With a warm roof the usual process is to split the insulation into two layers.
How to insulate an old slate roof.
A well ventilated roof space is good this stops your timbers rotting.
If 180mm is to be installed then 100mm board might be introduced between the rafters there has to be a minimum 25mm air gap between the insulation and the underside of the tiles or slates with an 80mm board running across the rafters.
The best way is to insulate the attic floor.
U value 0 38w m.
With an assumed pre existing u value of 2 23w m the best options are as follows.
If you want to insulate the sloping roof you definitely don t want to install spray foam against the back side of the slates.
Equally the reverse is true.
To insulate the roof itself you either use spray foam or retrofit with it with rigid foam board.
The materials used to insulate under the roof include batts of mineral or glass wool insulation held in place by battens of wood attached to and across the rafters.
Plasterboard 50mm pur insulation in 50mm timber stud with 50mm vented cavity to the existing wall.
If you want to avoid internal changes you can do so by insulating externally.
Check the depth between your trusses and the slates then install the correct thickness of kingspan in the gaps allowing for a 25mm air gap between the kingspan and the slates.