The arm band was worn by Police employed inside RAF Units and were RAF Station Police. Those employed outside Units were known as Provost Police and they wore The Black/red RAFP arm band. At the end of the War they were all amalgamated to become the RAF Police and would then wear the same arm band as worn today. For further info:
https://royalairforcepolice100years.weebly.com/
Here is an example of another style