I am not aware of any British or Australian law that would prohibit this. As a matter of policy RN warships are always made in UK but they don’t have to be. In this regard SSNR would be much easier than a US design, which would require a Congress vote plus separate presidential approvals for each listed technology.
Contractually with BAE based in both countries and an Australia UK trade agreement it should be by far the simplest option. UK shipbuilding law is summarised at this link.
A structured guide to shipbuilding in the United Kingdom
www.lexology.com
Remember the first SSN HMS Dreadnought was built using a US supplied rear hull including reactor. AUKUS could potentially see Australia doing the same in reverse now. UK has used Australian supplied Ikara and Nulka in warships in the past. So in future ASC could supply modules to assist UK SSN construction.
I think this is the most practical option by far. Off the top of my head the following relevant firms already have offices in Adelaide:
BAE - builder
Fraser Nash - detailed design of Astute class
Veritas - did verification of Astute SSNs
PMB - already contracted to supply batteries to RN
Lockheed Martin - presumably US combat system