No central Merchant navy personal records were kept between 1857 and 1913. The records covering the period of the first world war have been destroyed.
The only way of finding out what ships he sailed on is get hold of the last crew agreement he is entered on and back track crew agreements from there. Most would be in the series BT98 search via name of port. South Shields was always known as "Shields". Crew agreements after 1859ish some are in BT99 and others in MUN Newfoundland after 1863. Not an easy search.
Tried looking in the "CLIP" collection of Crew agreements available at FindMyPast. Are you sure he was born in London? There are several references there to a Robert Haydon Born in South Sheids in 1831. May be worth starting there.
There are apprenticeship records at Kew in BT150 (index) BT151 and BT152 (Apprentice fishermen) but not all have been preserved. TNA retained only those for every fifth year, some went to NMM Greenwich and the rest were destroyed.
The Society of Genealogists hold a collection of Indentures of many seamen from the North East dated 1845 and 1861. Collectively known as "Crisps Indentures" It may be worth getting in touch.
