arranfan
Sure, he might be going for trying to be like a rebel and aiming more at a media/political career. It might help, rather than hinder him. On the other hand, it seems like he is trying to speak as a doctor, with all the authority that gives him.
A formal complaint may not lead anywhere.
However, I can think of a few more conflicts of his Twitter behaviour with the GMC's Good Medical Practice. Because his way of addressing members of the "public," could legitimately make people worried about his ability to care for the individual "patient" in the following arenas:
31. You must listen to patients, take account of their views, and respond honestly to their questions.
32. You must give patients the information they want or need to know in a way they can understand. You should make sure that arrangements are made, wherever possible, to meet patients’ language and communication needs
33. You must be considerate to those close to the patient and be sensitive and responsive in giving them information and support
46. You must be polite and considerate.
54. You must not express your personal beliefs (including political, religious and moral beliefs) to patients in ways that exploit their vulnerability or are likely to cause them distress
It may be a reach, but Dr Harrop's behaviour online has undermined my faith in his ability to follow at least these GMC guidelines. It is not completely inconceivable that some kind of case could be built if there were enough voices chiming in regarding feeling that their confidence in him is low, and if one could link specific behaviour to each point. I think the hardest link to make is whether this behaviour has actually resulted in patient mistreatment in practice, but I do know that the GMC cares about the public image of the medical profession. I don't know if anyone wants to do this, or thinks it would be beneficial. And I really don't know what the GMC would do about it.
All I do know that I wouldn't trust that I would be fairly treated by him, if he knew my beliefs. And he makes me worry that he would be sexist towards me.
www.gmc-uk.org/ethical-guidance/ethical-guidance-for-doctors/good-medical-practice/duties-of-a-doctor