Several issues here OP.
Firstly, the police have a duty to act if there is reasonable grounds to believe an offence has been committed. In this case, GBH, if your assessment of injuries is correct. The idea that "no witnesses=no case" has NO basis in law. The CPS, having considered the evidence, may decide not to prosecute, but that's a different discussion.
The officers didn't do their jobs. If you don't believe me, suppose for a moment YOU were the victim, you had been beaten and punched, still think no arrests would have been made?
The officers were lazy/negligent and assumed your DP was drunk and abusive to the driver, happens every day, and based on this sexist assumption, they didn't exercise their police powers.
Firstly, make contact with the relevant Inspector, easy to find, just provide the officers collar numbers to the person on the phone and they can check who the supervising officer is. Then contact the Inspector directly. You need raise a complaint, not ask for an update.
The police are massively overworked, understaffed and they will always try to easy route of not investigating.
Be clear, there was more than reasonable grounds to believe an offence had been committed. You need to make a complaint.
Take the Inspectors name, be clear you are making an official complaint and NOT asking for an update.
Hope your DP gets better.