AR1,
Thatcher and her advisors failed to recognise the threat that was coming and there were questions being considered about the FI. To say she was on the way to dumping them is a bit of an illogical jump.
Corbyn's position on this has nothing to do with the UK's role. It is simply about his communist, unilateralism. Nothing more, nothing less. This latest statement of his is just a cynical attempt to disguise his singular aim.
Yes, the U.K. deterrent is independent. It is also part of the NATO alliance.