Sylvia, in the dim distant past when I used to research in London, Deaths at Sea from 1891 onwards were held by the General Register and Record Office of Shipping and Seamen, Llantrisant Rd., Llandaff, Cardiff CF5 2YS. They also held the records of enquiries into causes of death at sea, as well as births at sea (from 1891) and marriages at sea (from 1857).
The Guildhall Library holds manuscript records of some burials at sea 1894-1952.

Just had a look on the internet and it looks as though all except recent records have been handed over to the National Archives:
1891-1964 Registers and Indexes of Births, Marriages and Deaths of Passengers and Seamen at Sea, at BT 334.

See: webcache.googleusercontent.com/search?q=cache:5kGClrwievsJ:www.mun.ca/mha/research/principalrecords.php+cardiff+%22General+Register+and+Record+Office+of+Shipping+and+Seamen%22&cd=1&hl=en&ct=clnk&gl=au

I'll be interested to see how you get on.

Sue