Flat roof insulation

I am looking for advice on how to insulate an existing uninsulated flat roofed extension. I'm almost certain there is nothing between the plasterboard and the exterior material.

From what I can see the only options seem to be to take down the ceiling or remove the outside skin.

If you use hard polystyrene or hard polyurethane foam sheets on top of the existing roof cover (presumable bitumen felt ) than you have a better insulation for less money compared to just filling the space between the rafters. Both in combination would of course be even better.But if you need a new cover for the roof sooner or later than the insulation would be best on top of the roof. Covered with the skin of course.
If you take of a ceiling rosette (fuse!) you might be able to peep into the structure to see if there is already some insulation.