I think that there is a difference between sending abusive messages to or at a particular person or group with the purpose of offending and from publishing them

I think that there is a difference between sending abusive messages to or at a particular person or group with the purpose of offending and from publishing them to your own contacts and subscribers. For me one could (at least if repeated) constitute criminal harassment and the other is free speech. Some of the example you give fall on different sides of the line for me. Racist messages may be a different matter. It is pretty clear that the UK does not have free speech in that area (including face to face - inciting racial hatred is a criminal offence) and I'm not sure that is a bad thing although I would like to imagine it is better to hear everything and beat racism with arguments that sounds like a naive view. So from your list: Tom Daley - probably an overreaction. Angry tweet mob response probably sufficient. Prolonged harassment of less popular people in more need of police intervention. Carlton Cole - Potentially criminal on or offline. I wouldn't argue against police involvement. Praising Brevik - shouldn't lead to arrest (unless racist itself) although might get you watched. Dale Cregan fan - shouldn't be criminal just nasty and dumb. April Jones - Ridiculous. Unless posted to the family or on a memorial site. Soldiers - I don't think this should be a matter for the police or law enforcement at all. [EDIT - The Poppy Case is I think completely ridiculous and he should have just been ignored and not given the attention especially as it sounded (on the radio news) like he had just posted to his friends on FB. If he sent it to fan page for the British Legion or a support page for those who had lost family in conflict it may be worth the police having a chat with him although as a one off I don't think it should be prosecuted even in that scenario.]