When he reaches manhood, he will visit England. Is this sentence correct, or should the word "manhood" be replaced by the word "adulthood"?
Either is okay, though "manhood" instead of "adulthood" has the connotation that the reason to wait is because he wants to do something more associated (rightly or wrongly) with being an adult male than an adult female - drinking or chasing women, for example.
However, using "When he becomes a man ..." or "When he becomes an adult ..." is better. Even better, I would say, is "When he is old enough ..."
If there is a specific reason (implied or described elsewhere in the passage) to wait to go (say to be able to drink in the pubs), I would use "When he reaches legal age ..." or "When he reaches the age of majority ..." or (to be explicit) "When he is old enough to drink in the pubs, he will go to England"