I recently had a look at what has happened to arrest volumes in England and Wales. I've now looked at arrest rates, using force-level Home Office data by offence group for 2022/23 - here as a boxplot. Offence groupings are ranked by E&W arrest rate (L<R).

Arrest rates are calculated simply as (n arrests for the offence group / n police recorded crimes for that offence group) recorded in 2022/23. The Home Office arrests open data (most recent being 2022/23) aren't available at a greater level of granularity.