I don't think it is a modern problem. It's just more visible these days. Girls have been having sex (and babies) underage for years. Although to be fair, the age of consent was 13 until the late 1800s, so "being underage" was a lot harder then!
I think it is more visible and it pricks the public conscience more because 150 years ago we didn't have any form of state support (other than the Poor Law Unions, which typically meant the workhouse), and it was often managed within the family with the errant daughter being sent away to have the baby followed by it being brought up as a sibling.