What trade do I need?

Hi! I’m in the UK and I’m having an extension built. Unfortunately, it was started by the previous owners of our house before we bought it, so the drainage in the foundation is in a different place to where we want it (not even close). Since we don’t have access to mains sewage here, we have a septic tank.

I’m trying to figure out which trade we need to, firstly, install the drainage pipes inside the house (for the kitchen and a bathroom), route them outside through the wall and finally connect them up to the septic tank system?

Is that all the work of a plumber? Or would someone else need to do all or some of that? Thanks for any guidance as I have no idea!