Let's get this straight, I'm no fan of Cllr Gareth Compton. He's a Conservative councillor for Erdington and is, by default, wrong, possibly even as wrong as John Hemming.
But, sending the police to arrest him for questioning following a tweet is a waste of time. Was it offensive? Yes. Was it a daft thing for an elected representative - or anyone else - to say on what is, after all, a public forum? Undoubtedly. He has apologised for any offence caused and that should be an end to the matter. Any further punishment should be in the hands of his party - which has already suspended him - and the electorate in Erdington.
Let's bring some perspective to bear on the matter - nobody was actually going to threaten any form of injury to Ms Alibhai-Brown as a result of seeing Gareth's tweet and I think it rather unlikely that he would make the journey to carry out the deed himself.
On a day when Paul Chambers, who has been punished for an equally unfunny joke tweet about Robin Hood Airport, lost his appeal and found himself saddled with additional prosecution costs, as a further punishment for his challenge, this sort of legal behaviour brings the system into disrepute. The law needs to be changed to consider intent - neither Gareth nor Paul Chambers had any intent of causing injury or loss. Both tweets failed a humour test, but that is not cause for criminal prosecution.