Ships like HMS Worcester trained Cadets pre sea on the grounds that they would be taking naval exams for Royal and Merchant services , but the fact that he became a galley boy , makes me think that the Arethusa i a training ship established by Lord Shaftesbury in 1874, to join her sister ship, Chichester, at Greenhithe is a better bet . Lord Shaftesbury was a campaigner for social reform, and ran shelters for homeless children in London.Shaftesbury viewed training ships as a way of securing a trade for boys who would otherwise have had little education or future. He appointed a shipping agent, with the aim of finding places on board suitable ships for his boys, mainly in the Royal Navy but the Merchant service was an option .Due to the location I would "Guess " that the national Maritime museum may have details of entrants . As this training was School like rather than sea service there would not be a discharge or log book record . These training ships were permanent units immobile to all intense and purposes . There is a book on the subject ‘Nautical Training Ships: An Illustrated History’ by Phil Carradice . There were several and I am sure that there was ones in the Solent and Plymouth as well as the Mersey , At a good Guess start trying the Arethusa though , as right place right time right circumstances . that may lead to the other choices