How old is Billy supposed to be?

About 20? I think the point being made is he's under 21.

Tom Courtenay was 26 when he made the film but looked to be in his early to mid thirties. He looked as old in Loneliness of a Long Distance Runner. If he had looked nineteen, I might have felt a little more sympathy for such a daft character, but he looked too mature for me to feel, "he's just a kid". The part was so demanding however, that it required an actor of Courtenay's ability and that's a rare thing. So I'll settle for a well-acted, less sympathetic Billy over a kid who couldn't act the part.

About nineteen - one of the generation who missed out on National Service.