Builder or Plumber? Open drain in Conservator or Lean-to

Hi, I have an open drain in my conservatory/lean-to. All it does is take waste from my kitchen which is the other side of the wall. I would like to either move it, or somehow relocate the kitchen waste in another method. I'd evenutally like to use the space as a home office, so really don't want the sound of running water everytime the washing machine is on, or someone's using the sink. Do I need a plumber for this, or a builder? I'm expecting that the flooring may need to be dug up to re-route so wasn't sure if it's more a builders job, or a plumbers.