Regarding what weas has advised:
Now, please believe me that I'm not trying to take the side of the Police, nor anyone's for that matter. However, before doing anything rash, you should consider the following:
1: Were any of you under the influence of alcohol? It could have a bearing on any subsequent complaint.
2: Is there any CCTV to "back-up" your claims of the alleged excessive force used.
3: Bearing in mind that you've mentioned "about 15 people fighting", it may seem to a reasonable person that the Police were justified under the circumstances in handcuffing anyone they arrested for fear of theirs, others present, or indeed the arrested person's safety.
4: It's the easiest thing in the world to make a complaint against Police for something which you and/or others may perceive as some kind of wrongdoing. Don't forget, though, that not only would it have to be proved by whoever makes such allegations, but the Police's version of the incident will undoubtedly vary drastically to yours.
5: In the cold light of day, can you, your partner and any of your witnesses honestly say that none of you did anything wrong? If you CAN, then go ahead and make your complaints. But if you have any doubts, given that your partner you say has been charged with a serious Public Order Offence, then I would think again if I were you.
6: The Law is there to protect everyone, and that also includes the Police. They are not entitled to act outside it, but neither is anyone else.