BAE (f.k.a British Aerospace) said on the day of the AUKUS announcement it is prepared to participate. That doesn't sound like a company that has been closely involved in the negotiations.
In all likelihood the Australians will pick US Virginia-class subs off the shelf, not made in Australia and not the (excellent) British Astute-class subs, because the US doesn't normally let junior partners get the spoils, only crumbs. For instance when the US organized the 1953 coup that overthrew the Mossadegh government in Iran at the British' request, the Anglo-Iranian oil company was replaced with a consortium of US and European oil companies, with the British getting less than the would have had if they had accepted Mossadegh's most maximalist plan).