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.

I've then gone a stage further and looked at force-level arrest and (crude) charge rates. Higher arrest rates are associated with higher charge rates for most crime groupings, especially theft, robbery and public order offences. (E&W overall = red dot)