The commission’s report stated: “While we consider that there is a serious problem of crime that is connected to misogyny, we have concluded that the particular model of hate crime laws is unlikely to prove an effective response to misogynistic offending, and may prove more harmful than helpful, both to victims of violence against women and girls, and also to efforts to tackle hate crime more broadly.
“We suggest that reforms in other areas are more likely to result in tangible, positive results.”
In a written statement, Ms Dines said: “The Government agrees with these concerns. Accordingly, the Government does not intend to bring forward legislation to add sex or gender as a protected characteristic in hate crime law.”
https://www.independent.co.uk/news/uk/government-christine-jardine-home-office-misogyny-liberal-democrats-b2326445.html
I am not sure where the written statement is, but might be this one:
https://www.parallelparliament.co.uk/debate/2023-04-25/commons/written-statements/law-commission-review-of-hate-crime-laws-recommendation-8