Their service records are held by the Ministry of Defence and are not available elsewhere for privacy reasons. http://www.nationalarchives.gov.uk/help-with-your-research/research-guides/royal-navy-ratings-after-1928/
is a guide from the National Archives that includes a link to the MoD website where you can download the form to request a copy of their records.
However please note that for similar privacy reasons, you need permission from their next of kin to access the full data otherwise you will not get a full copy.
The National Archives have other research guides for the Royal Navy that may help you access details about operations in the Second World War.
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