JustcarInsurance has a list of assessors/repairers, they called me and let me pick which one to use. I just picked the closes one to my house for easier transportation, you pretty much deal with the assessor which is the owner of the repair workshop in my case. How easy going the workshop is dependent.... You don't actually deal with an assessor directly from JustcarInsurance, just a workshop which is contracted to justcarinsurance.
That's from my experience, could be different though.