It seems to be a law without teeth though, as proving it must be a nightmare. My ex was emotionally abusive to myself and my dcs, but always in our house or in the car, rarely did he slip and do it in front of others. Once his mother started having memory problems, I noted he was less careful in front of her, which I assume was because he then felt he could pass off any comments she made as a faulty memory.
Even his own family, who have witnessed a few slip ups on his part, and who have remarked on his dreadful temper, deny that he could ever be abusive. If I can't make his family believe, when they witnessed a small part of it, how could I ever convince the police? It's his word against mine, and he has a very finely tuned "public persona" that he puts on in front of others.
Having worked for the police, I've seen the attitude from quite a few PCs that they very clearly attribute any domestic situation as "not a real crime" and the eye rolls when talking about the woman and her saying she is being harassed and threatened is truly disheartening. I said something each and every time, and got a bit of a reputation for crusading the domestic situations a bit, but I've been there and it's terrifying to be stalked and harassed and threatened. Until domestics are regarded as serious across the board and the police are required to deal with it better, I don't see it improving much.