You claim, and object, to the UK being tied to US missile and targeting technology - then suggest we adopt the use of a SLCM-N as a deterrent? Extremely muddled thinking I feel.
The current Tomahawk missiles are conventional only, and the components including the engine are cheaper versions than those previously used up nuclear versions. Adoption would need the design if a completely new version meeting all the nuclear safety criteria - outside the knowledge base of UK designers. The USN is investigating the design of a new nuclear SLCM, but that is many years away - and in any case either choice would also depend on US missile and targeting technology.