Hi Kew, and welcome to the forum.
As far as I'm aware there are no insurance companies that will automatically use Audi (or any other manufacturer) approved repair centres per se, but you have the power to insist on it. The only objections they raise are that if you choose the repair centre the insurance co. will not supply a loan vehicle, but as all repair centres these days supply one of their own this is not a problem.
Obviously if the Audi approved centre quote is significantly higher than the insurance co. expect you may have to "discuss" this with them, but this should not be a major issue.
Having a good insurance broker helps enormously with this and they will also find you the cheapest quote with a good insurance co. I've used one for 30 years plus and have found them an absolute boon, both in terms of money saved and administrative headaches prevented.