The Home Office does not hold the information requested centrally.
The Home Office collects and publishes information on the number of police officers on certified long-term sick absence as at 31st March each year.
Long-term sickness includes any recognised medical condition, physical or psychological, as reported by the officer or a medical practitioner, which has lasted for more than 28 calendar days. These data are published in the annual ‘Police workforce’ statistical bulletin, available here: https://www.gov.uk/government/collections/police-workforce-england-and-wales
However, these data do not include the reason for the sick absence therefore the Home Office are unable to identify those on sick absence due to injuries occurred at work.
The Home Office also collects information on the number of police officers on short/medium term sick absence as at 31st March each year. Short/medium term absence due to sickness includes officers on leave for 28 days or less. Again, these data do not include the reason for the sick absence.
This information is published by Her Majesty’s Inspectorate of Constabulary and Fire and Rescue Services (HMICFRS) in their Value for Money profiles, available here: https://www.justiceinspectorates.gov.uk/hmic/our-work/value-for-money-inspections/value-for-money-profiles