There was no official registration of merchant seaman between
1857 and 1913. The Merchant Navy began to register its seamen again in 1913, in the central indexed register, or Fourth Register of Seamen. However, the entries for 1913 to 1917 have not survived. Therefore neither TNA or any other institution have these types of records. Simply they do not exist, apart from some officers records but that's another story.
The only way of finding individual Merchant Seamen's records in this period is via Crew Agreements.
This can be a long, time consuming, frustrating and sometimes expensive exercise.
If we follow on from the references to the deaths of individual seamen contributed by Stevie Steve. There was a Mate with the surname
Copeland lost by drowning on 26/10/1871 from the Steamer BIAFRA, official number 60847, which was owned by the African Steamship Co Ltd.
If this is your man. His death will be recorded in one the
Logbooks and personal details of him, place of Birth, NOK,
previous ship etc. in the vessels Crew Agreements for the relative date in 1871.
These are available at a fee,from MHA in Newfoundland.
https://www.mun.ca/mha/holdings/viewcombinedcrews.php?Official_No=60847You can then hopefully backtrack via the previous ships crew agreements till you have a total record of his sea service. Almost without exception British and Empire ships Crew Agreements are stored via the vessels official number.