I am so sorry, js. Your poor daughter. Poor you.
This website is aimed specifically at teenagers: thisisabuse.direct.gov.uk/ . It has various contacts here.
Childline can support your DD if she wants to chat online or phone them. There is also a website called The Hideout which has been created by Women's Aid to support children and young people.
You can also ask your GP to refer her to counselling. If your GP can't, the NSPCC or Women's Aid may be able to help.
You may also want to help your DD make a safety plan. This basically involves thinking through possible risks/worrying situations in advance (e.g. bumping into him at school, him trying to hurt her again, etc.) and deciding what she wants to do if the worst happens, and making sure she has 'phone numbers and anything else she might need in a future emergency.
I would want to go to the police, too. But I will be a slightly dissenting voice here and say that I do think it needs to be your daughter's decision. DV is not just a violent crime, it is also about misuse of power. Your DD will be feeling very dis-empowered right now, and as her parent, you need most of all to help her feel re-empowered again. Having a choice about what she does, and being supported by you to make the decision (and to change her mind if she wants to) will probably help her. On the other hand, if she really does not want to go to the police, and you force her to, you may add to her feelings of powerlessness.
FWIW, I have some experience... My eldest son has been beaten up by known people three times. The first time I did not let him make the decision, and I called the police and the school. The police investigated and interviewed the perpetrator and other children (it happened as kids got off the school bus and was witnessed); but there wasn't enough evidence for them to take action, and my son (and I) felt very let down. The school 'kept an eye on things' but nothing more. My son was very angry with me, and said it made things more difficult for him because he became the subject of gossip, as the older boy and others talked about what had happened, and laughed about him 'needing his mummy' to sort things out. :(
After that, I let him decide what he wanted to do, and each time he decided he did not want to involve the police.
The sad truth is that DV is even harder to 'prove' and prosecute than other forms of assault, because it tends to happen in private with no witnesses. If you/your DD decide to go to the police, please try to keep her expectations low because it is unlikely that he will be 'punished' much or at all. :( I think she needs to understand that she is reporting him because she wants to take a stand/'stand up to him', and because it might help protect other girls in future, but that it might not lead to much or 'fix' anything for her.
I wish 'the system' was better at dealing with these situations - I think young people are badly let down when they are victims of crime.
Good luck.