Joist noise from Neighbours - Shared joists

[MrZ]

Hi
Have also posted this is timber section.
Would really appreciate some advice for a structual sound proof problem.

I live in a Victorian terrace. The hallway, stairs, landing etc are adjacent to my neighbours hallway, separated by the party wall of course. The party wall is single width brick

The floor of my hallway is made up of exposed floorboards over a suspended floor above a cellar. As the lath and plaster is missing in the cellar ceiling i can see that the joists spanning my hallway disappear into the party wall and appear to continue across my neighbours hallway in one continuous span. There are maybe 10 joists in total in the hallway, hallway is about a 90cm wide

The problem i have is that my neighbours are really heavy footed and have 2 kids who run about with their shoes on and jump off stairs into the hall etc

Given that the joists span both hallways this impact noise transmits straight across the shared joists into my house and is really intrusive. One of the joists is now deflecting so much (it has gone a bit crumbly) that the whole of my hall floor creaks really loudly when they walk about.

At the very least i want to replace the crumbling joist, ideally i'd like to "separate" all the joists somehow from my neighbours or get new ones put under the hall on my side so that the impact noise from next door is reduced.

I clearly cant just cut and replace the joists as they go through the party wall and under my neighbours hall too. No doubt the Party Wall act will play a part too.

Can anyone offer some advice on how i would go about this. ie. Could i just agree with neighbour and get a builder in, or would i need a structual engineer to assess things first etc?

thanks