There was no central register of seamen. It may be possible to find something from crew lists or log books (BT 99), but we only have a 10 per cent sample of those.
Merchant Shipping: Crew Lists and Agreements, 1747-1860
Merchant Seamen: Agreements and Crew Lists after 1861
My Ancestor was a Merchant Seaman, Second Edition, Christopher T. Watts and Michael J. Watts (Society of Genealogists)
Another 10 per cent are at county record offices. Some hold agreements and crew lists for ships registered at ports in their area (1863-1913).
A further 10 per cent are at the:
National Maritime Museum Maritime Information Centre Romney Road London, SE10 9NF Telephone number: +44 (0) 20 8312 6712
The rest are with the:
Maritime History Archive Memorial University of Newfoundland St John's, Newfoundland Canada, A1C 5S7
The Maritime History Archive has an online catalogue of their holdings and of those at county record offices.