Don't actually see any new laws being made, although misogny might be an aggrevating factor in a Court Case if it was deemed a hate crime, although that would need new Parliamentay Ammendments to Legislation.
If you examine the two arrests so far one was for public order offences and the other actual bodily harm, both already offences in the UK.
Other offences that could be used include harrasement (sexual) and common assault.
What should also be remembered is that the police in the UK have no power to prosecute, everything has to go though Crown Prosecution Service (CPS) Lawyers who decide whether to prosecute and put the case before the courts or to discontinue it, and for those cases that do proceed to the Courts it is for Judges and indeed in more serious cases Juries to decide on such issues. It also should be noted that people accused of criminal offences in the UK qualify for Legal Aid and a Lawyer and many Lawyers would relish taking on cases of misogny of all things, something which might be very difficult to prove in a Court of Law.
So it's not up to police forces to make the Law or to determine the Law, that is for Parliament and the Judiciary, so a Police Force can not just decide that Misogny is a hate crime and should be an aggrevating factor, that is for Parliament and the Courts to decide.
misogyny | University of Bristol Law School Blog