it is not unusual for bays, especially on the upper floors, to be a timber frame with tiles or boarding on the outside, and a plaster face on the inside. However you say that yours has a brick outer leaf.
Luckily, this not a difficult building job. Insulation can be put between the two skins, and a vapour barrier incorporated on the inner wall to prevent warm, damp air from the room getting into the gap and causing condensation.
It may be useful to pack mineral wool between the joists where they go into this cold space, to prevent cold air blowing under the floor.
I think you said on another thread that yours is a Victorian house, so most likely the walls are 9" brickwork with no cavity, so they are bound to be cold. It is possible to dryline the internal surfaces of the external walls to reduce heatloss, this will add several inches thickness. Rigid foam slabs of insulation are usual as they insulate better than the same thickness of mineral wool.