In those days the Navy was geared towards closing Iceland/Faeroes gap to Soviet subs, in the event the the balloon went up. It was fairly routine (I believe) for FF/DD and carriers to carry nuke depth charges to counter this threat. According to the news stories I heard, they made an early decision to unload the nukes, as I suppose it would of been very difficult, politically speaking, to be the first country since 1945 to use nuclear weapons, especially as our existence was not threatened. The report said that the Nukes were unloaded at sea, so I assume they were taken off by RAS. The reason it came to light was that some of containers were damaged during the transfer.
http://news.bbc.co.uk/2/hi/uk_news/3295855.stmr.