Insulate behind existing dry lining.

[CotswoldDoItUpper]

The old bit of our house has solid walls approx 800mm thick and was battened/dry lined on 2in x 4in frame in the 80s with no insulation.
 

My wife is adamant that we aren’t removing the plasterboard or adding anything on top, and I’m trying to find a way to insulate. 
 

how (if at all) can we both be satisfied?*
 

* I would request to keep it clean, but from my experience so far think this is unlikely! 😂