Its what is know as "uninsured losses" i.e. your excess and your NCD

You need to speak with your insurance company as i assume you have provided them with insurance details for party A to see if they will pursue your uninsured losses from Party - as you are fully comp this should be a given but just check.

You should also see about getting a hire car paid for by Party A as you car is written off as they are also liable to cover that as well.

I had this happen to me a few years back where someone hit from behind and i had a hire car, uninsured losses recovered and no affect on my NCB.