The Maritime Libraries post seems popular, so I've asked for permission to add content from the book. Keep an eye out for future posts that highlight various archives around the UK.
Disclaimer: as this material was published in 2004, I have tried to update the websites (2016), but internet addresses often change.
The title is:
Maritime Information : a guide to libraries and sources of information in the United Kingdom. by Fenton, Briody and Macdonald. 2004. 1901703452
British Library - Oriental and India Office Collections
Special Collections: East India Company, 1600-1858; Government of India, 1858-1947.
British Library of Political and Economic Science, London School of Economics
Special Collections: Papers of Charles Booth, Liverpool shipowner, relating to his social investigations in London; Shipping register of J. Byrn, c. 1809; Ship account book of John S.P. Mills, master of steamers Striver, Runnelstone, and Charlwood 1920-1926; Report on shipping control in First World War and subsequent correspondence of Sir K.S. Anderson, manager of Orient Steam Navigation Co.; Papers of the Inland Waterways Association, 1917-1983; Papers relating to political and foreign affairs interests of Edmund D. Morel, 1873-1924, shipowner; Business documents of Robert Newman and Co. of Dartmouth, traders with Newfoundland, 1774-1955.
National Army Museum
Special Collections: Hodson card index includes biographical and service details of officers of the Indian Navy and ship's officers of the East India Company's fleet up to 1861.
Society of Genealogists
Special Collections: GRO indexes to marine births and deaths, 1837-1965; Navy List, 1756-1990s and East India Company naval personnel, c. 1760-1833; Trinity House Petitions, 1750-1890; Apprentices of Great Britain, 1710-1774 ; PCC (Prerogative Court of Canterbury) will indexes to 1800 (containing wills of those dying at sea).
Maritime Libraries in the UK :
Aberdeen, Cumbria, East India Company, Liverpool, Shipwrecks, Wales
“Reproduced by kind permission of the Maritime Information Association”