Any of us could fall foul of this law if it suited someone to complain to the police and if it suited the police and the CPS to pursue the matter.
This is a catch-all law.
It's illegal to cause annoyance, inconvenience or needless anxiety to someone by the persistent use of a public electronic communications network. The courts have ruled that social media platforms such as twitter or fb are public electronic communications network. Persistent use would include your responses in any prolonged argument you get into, with anyone, about anything, anywhere on social media.
I wonder if the courts would decide that forums like Mumsnet are public electronic communications networks. I see no reason why they wouldn't be, if twitter and fb are.
Some people on this thread are causing me annoyance right now.