Sorry, yes meant SSNs rather than SSBNs... Though anti piracy ops using a SSBN would put the wind up the buggers
The crux of the issue is that everyone starts with equipment and then works back to the requirement.
14 world class AAW and ASW vessels is more than enough to defend UK Territorial waters, and also support a 100% available world wide CVBG/ARG which would only be 2nd to the US in terms of capability.
The question should be what is the RN's role outside of these high end activities and what kit is required.
Assuming the RN does eventually get say 12 MHPCs (replacing the MCMs, Echos and Rivers), outside of UK EEZ / Fishery patrols (3 vessels), Falklands patrol ship, Clyde MCM, worldwide survey (2 vessels) and Gulf MCM duties (say 3 vessels) - what is left for other tasking? Probably, one max.
So if you go down the 5 GP T26 route, you can probably say two at one time will be available - so at best a total of 3.