Births, marriages and deaths at sea
Records
The National Archives
The National Archives holds a number of series relating to BMDs at sea. Details can be found on the Your Archives wiki.
Records include the open-access microfilm series BT 158: Births, Marriages and Deaths at Sea 1854 - 1890 British Subjects and Other Nationalities. More details of BT 158 are included in this FindMyPast article (scroll down) which advises that there are many entries detailing events for men serving in various British Army regiments and the Indian Army, together with births and deaths of Regimental Wives and their causes. As an example of births in the period 1854 to 1858, the birth of twins to Joanna Wedderburn the Wife of Andrew Wedderburn of the Madras Civil Service.
TNA also holds the Colonial Office Registers of Births and Dates of Emigrants at Sea