Assuming you do have to insulate internally, "breathable" is too simplistic - this means "vapour open", and you risk interstitial condensation on the now cold solid wall. The options are to use a vapour control layer (VCL) or an insulation that wicks moisture back into the room. In a retrofit the VCL is hard to seal at joists etc, and if not sealed then moisture can get round your barrier, so the alternative is worth exporing - try Ecological Building systems for products and advice. Other issue is rain absorbtion by the solid wall - this may want treating with a sealant - once you insulate the wall it isn't so warm and doesn't dry out so easily.
As to insulation levels, you will probably be reaching U-values of 0.3-0.4 on the solid wall, can be risky to try lower, but this doesn't mean you shouldn't aim for half the heat loss on the newbuild, ie U 0.15 -0.2. It should be easier and cheaper to achieve a given U value in the newbuild, compared with retrofit, though given the area of old wall you need to do a reasonable job there too.