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Either dyna mat on the walls before putting units on, or you could do a full wall of equastrian/horse rubber floor matting. Mass, lots of mass helps deaden sounds, thick shredded rubber does make a difference. BUt as already said, that kind of foot step sound will travel through every solid surface quite nicely.
Redid a party wall in a flat. Was just 80mm stud with plasterboard on both sides and some insulation inside. Made it into 120mm stud, double plasterboard either side (fire reg), regular insulation inside and one sheet of rubber horse floor matting, and a 50mm PIR foam insulation on my side for extra warmth incase flat next door becomes empty for any time. Made a huge difference against talking/human sounds. Can still hear some stuff, but it sounds like its a whole extra room away instead of 150mm away. Lost a bit of space from room but worth it.
Got a flat in a 1940s concrete and brick block which I'm totally renovating. Since moving I've realised that I get noise through the walls that face the common stair place. Main problem area is the kitchen, but there's definitely flanking because the ceilings and other walls are also brick and concrete. The ideal (but unobtainable solution would be for the stairs to be properly lined because it's noise from hard shoes that reverberates, not talking or other airborne noise. Can't afford (money or space) to do a full job of a suspended wall with loads of gap, sound insulation etc. Kitchen units will go against the wall which might help a bit, but wondering if it's worth me losing 20mm of space to line with a heavy vinyl mat and then green glue on some 12.5mm acoustics plasterboard. Anyone tried that? Good money after bad or worth a punt because it might at least soften the clank of heavyset people in stilettos coming down the stairs?! Any advice appreciated!!