They are indeed subbied into T-N, much the same as Thales is subcontracted to the PCO (despite it being a partnership...
). However, when I was there they were indeed doing the design work on CADDS5.
I may be wrong but I will be
very suprised if the shipyards end up doing any design work, for the simple reason that at some point all 5 super blocks (or whatever they are called today) will have to be joined up, and if a VT draightsman has drawn a pipe in one location, you can be sure that a Babcock draughtsman has drawn it in another. Configuration control in that situation would be a living nightmare. Far easier IMO just do all the drawings/design at the PCO and then distribute them to the relevent shipyards. At least then (in theory) everything shoud join up at the end.