The designer is the person who is experienced enough to design it to your needs, planning constraints, and building regulation requirements. And do all this cost effectively. This might be an Architect, an Architectural Technician, building surveyor, structural engineer, or anyone who is experienced in the design of buildings.
He will also know if the Party Wall Act applies, if build-over agreements are needed and if engineers need to be involved. He will also know how to design to avoid any of these if possible.
He will know whether to use the council inspector or a private one, and he will know about all potential fees involved, not just the build cost.
This is not the builder who wants as much money out of the job as possible, or who does not want the job or who wants to do it his way.
Your first step should be to get a proper assessment of what is possible based on the site constraints and your budget. It's no good getting an estimate or a even a fixed quote on something that can't even be built.
Bare in mind that someone who can draw plans is not the person you need. It's more than that.