here is an address where the records are kept,
Goliath and Exmouth — London Metropolitan Archives, 40 Northampton Road, London EC1R OHB.
her Majesty's ship the Exmouth, lying off Grays, in Essex, which has been instituted as a training ship for boys chargeable to the poor rates of the metropolitan parishes and unions. The Exmouth takes the place of the Goliath, destroyed by fire last Christmas twelvemonth, but is under different control. A few East London parishes, under the name of the "Forest Gate Stool District," in order to provide a marine training for boys
if you type ''training ships goliath and exmouth'' into google you will come up with the link below with pictures of the boys and ship etc. also many other related sites i cannot post the pic's as they are copyright,
Training Ships Goliath and ExmouthA few East London parishes, under the name of the "Forest Gate Stool District," in order to ... Training ship Exmouth, 1917. Exmouth boys at drill, c.1929 ...
users.ox.ac.uk/~peter/workhouse/MAB-TrainingShips
all the best, kali.