It used to be the norm that you got 3 quotes and the insurance company would choose the cheapest one. Though nowdays, the insurance companies normally have their own contacts who will carry out the work. Like if you wanted a new cooker, fridge etc, they would tell you what companies/shops they deal with, and you would have to go to them.
My friend had a similar situation a couple of years ago, downstairs ceilings and upstairs floors had to be replaced after flood in bathroom. Insurance company made assessments and used their contractors - even carpets had to be replaced and my friend was told what companies she could go to. I think why this is done now, is because years ago people would make on the deal, by putting in false estimates and actually getting work done cheaper.