Sorry to hear about your accident. Got my NX back yesterday. Although dealing with the bodyshop was a pain in the backside, I would never use Admirals "approved" repairers.
And stay well clear of Albany. They were very insistent that I use them for my courtesy car and wanted me sign credit documents. They charge an absolute fortune and if the third party's insurance contest the cost, you're in a whole lot of bother.
As rayaans pointed out earlier in the thread , it's your right to choose your own bodyshop. Go to your nearest Lexus approved bodyshop and give them the claim number and they will do the rest. Also ask your Lexus dealership if they will provide a courtesy car if the bodyshop doesn't have one available.
Hopefully it will be a smooth process.
My issue with the bodyshop was the lack of communication, thats why I made a complaint to Lexus GB and after that my car was fixed within a few days.