To add to Steven's answer we use this phrase in the same two ways in the US. In fact, the second one is much more common.

"To tell on" can have two different meanings. 1) to have a bad effect on someone's health (or similar), e.g. "He had to work late every night and the stress was beginning to tell on him" 2) to give information to a person in a position of authority about someone else's bad behaviour, most often used by/about children. e.g. "If you try to pull my hair in class again, I'll tell on you (to the teacher)" Meaning 2) is quite colloquial and may be UK-specific, I'm not sure.