I know a good bit about one such training ship, the Exmouth. Many of them were reformatories, but some, like the Exmouth and your man's, took boys from disadvantaged backgrounds and gave them a training for life at sea. If you google on "training ship Exmouth" you'll find a lot of information. They were shore-based, by the way; only occasionally did the boys go to sea.
The Northumberland archives would probably be able to tell you what ship he may have been on (assuming it was local), but whether records survive is another matter.
About 30 years ago (gulp!) I wrote up some research that a friend's husband had done on his father, who had been a trainee on the Exmouth. We published the article in the magazine "Sea Breezes" and I got a number of responses from all over the world from men who had been trainees. It was fascinating stuff.