It also found the programme failed to act in the best interests of the child, even if the mother had given consent.
"Children should be seen as individuals in their own right and not as attachments to their parents. We do not consider in this case that the broadcasts were in keeping with the best interests of [the child]? A cautious and sensitive approach could have been taken, and in our view, ought to have been taken," the BSA concluded.
The BSA recognised the value and public interest in the story but said that was outweighed by the need to protect the son.
Freedom of expression needed to be weighed against other rights, especially if children were involved, it concluded.
"In our society and in our law, when there are clashes between rights and when included amongst the rights in clash are the rights of children, the rights of children almost always prevail.
"Children are especially vulnerable. They cannot protect themselves and societies have the most powerful of obligations and reasons to look after their children who are their future," the BSA concluded.