I suppose it sounds worse at the moment as we have the room totally
stripped, walls are channelled for sockets and comms, bare boards and
some fresh plaster.

Im planning on gluing a sheet of soundbloc or similar plasterboard onto
the party wall with gripfill (pinkgrip better? non-slump?) recesses
upstairs and down. It cant hurt. Floor will probably be new wood with a
good underlay and rugs because the cat has the habit of coming in from
the garden and chucking up. Dont fancy spanky new 1500+ pound carpet
getting ruined within days!

Yes I know I should have an air gap, insulation, stud wall and two
sheets of plasterboard but it will ruin the character of the room and I
dont want to sacrifice the space.