I can sympathise with you. We have experienced the same thing although it has got better in recent years and we don't notice it any where near as much now. Yes, our neighbours also have a heavy foot print at times but I couldn't say it is extreme. If we keep all our sounds sources off though, you can hear their telly and muffled voices. We certainly can hear their phone ring.
So ours is a 1930s semi also with a double brick 9" party wall. Most of the properties in the road are built similarly and from those neighbours I converse with, they can experience the same sound permeability as us.
The layout of our semis means the front and back living rooms from either side are adjacent with the hallways to the outer walls. This layout means you are closer together from the start.
From what I can gather a well built 9" party wall is pretty solid and relatively sound proof. However, poor detailing and any pockets or missing bricks scattered around will have a big impact.
Given the size of the pockets for purlins in our loft space plus a few missing bricks in the party wall where you could see straight through into the neighbours loft, I suspect there will be some leakage points in your house and ours.
I have tried to stand at our wall and identity where. But it is very hard as the sound reflects off surfaces so you can't really tell. Next door have no floor coverings only floor boards from the wooden suspended floor. I strongly suspect there are open pockets to next door in party wall below floor level but I could not face lifting all the boards whilst we were doing an extension.
I can also say, in our front room, the previous occupiers had battened out for mineral wool and double plasterboard, this is also done in the bedroom above. When noise is a problem it does not really make difference, in quite or moderate noise it attenuates a little but not a huge amount. This is another factor why I suspect sub floor and between floor areas of party wall. You may wish to investigate the party wall hidden by the ceiling or the subfloor area before spending on trying to soundproof the doubleskin brick and plasterwork.