Sure, and that's an overreaction.
But the loss of his job is presumably a matter between him and his employer, not the supposed "PC gone mad" state. People have been sacked for even less in terms of internet communication.
As far as getting arrested is concerned, just imagine if there was an airport bombing, those tweets had been there, and nothing had been done by the police. That's the risk management angle. That doesn't even have anything to do with regulating free speech, the charges he faces are just the consequences used to justify the action taken on another account.
The Communications Act 2003 seems to be a rather wide-ranging and ridiculous curtailment of public expression, I'll grant you that.