Cavity wall insulation on tile hung wooden frame upstairs

[xfon123]

Was wondering if cavity wall insulation is an option in my house? Upstairs is wooden framed built on a brick built ground floor. The upstairs walls are lath and plaster with the external walls closed boarded and then tile hung. There is a good cavity between the lath and plaster and the closed boarding but wondering if I go with cavity insulation will I have a moisture problem and it will affect the the lathe and plaster? Need a solution as currently is much colder up there.

Any help much appreciated or other suggestions???

Thanks