The Royal Navy Research Archive General Message Board
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It depends on which time period you are interested in. I am presuming that it would be World War 2?
If it is for service after 1938, then they are held by:
Data Protection Cell (Navy)
Victory View
Building 1/152
HM Naval Base
Portsmouth
PO1 3PX
Tel: 02392 62 8671
They do not normally release details to non-relatives, and a small fee is charged for the service.
I would suggest that you contact them.
If it is for an earlier term, then different authorities are responsible.