A continuous 40mm semi rigid woodfibre batt thermally isolates the timber studwork from the (external) masonry party wall to the west with further woodfibre batts between and being water vapour open (and with the lime parge) should be a long term robust solution.  The east party wall is more complicated due to the elevated risk of damp due to the neighbour’s chimney stack and the MVHR ducts so vermiculite was poured all the way down the chimney flues and continued up to insulate the wall in the loft.  vermiculite doesn’t have quite as good thermal performance but it’s ability to flow into every area was critical and should stop flanking noise travelling up the chimney flues and negating efforts made with the floors!