Okay Jean,
The records of the Royal Navy will be found at TNA Kew London, they also hold the records of all the government departments that administered the Royal Navy from its very begining.
The National Maritime Museum also in London and the Royal Naval Museum at Portsmouth may also be of interest.
From the dates you give, 1897-1908, the 75 year rule of confidentiality does not apply, so you should be okay.
The Royal Navy was reorgananised in 1853 and each new recruit was issued with a unique continuous service number.
From 1894-1923 this changed and they issued numbers in groups for each of differant branches.
They are as follows;
Seamen and communications ratings JI-J110000
Engine room artificers and Artisans M1-M38000
Stokers K1-K63500
Stewards, Cooks boy's etc L1-L15000
Short Service Seamen from 1903 had the Prefix SS1
Short Service Stokers from 1903 had the prefix SS100001
So you will find his name in the Register of Seamens Service's in ADM188,
you may also find (if he served at sea!) a look in the Ships muster books up to 1923 would prove worth while, these are in ADM36-ADM39 and ADM41,115,119.
Hope this helps
Frank.