Ok, Stu, I'm not a lawyer, and it may be that you are and know better, but as I read it your link says that the Telecommunications Act in s43 (1) (b) makes it an offence to send by telecomms a message THAT YOU KNOW TO BE FALSE and to cause annoyance to others by persistently doing so. The header on the description of that part of the link mentions causing "gross offence" or "menacing character"..
If we presume that it is in fact correct that the original poster's son owes money to the bank I fail to see how that applies? Unless they are actually threatening or menacing the original poster.
Anyway, as I suggested before, would it not have been far simpler for the son simply to call the bank if it's annoying his parents so much?