You'll be incredibly lucky to find an RHD one let alone a LHD. I tried a few years ago to hire a vehicle in the UK to drive to Turkey and wasn't able to. You need a V5C in your name to bring the vehicle into Turkey. You won't get a hire company to sign the vehicle over to you.
You seriously need to consider alternatives. Have you thought about buying a vehicle, driving it over and then either signing it over to the Belediye, or, driving it back yourself or getting someone to accompany you, so that they can drive it back? The purchase costs and hire costs, together with shipping costs, can be comparable.
I trust that you're aware that you need to have a Residence Permit to import your personal belongings ?
When are you thinking of making this trip ?