Hi Pat,
The only force to still wear 'Duty Bands' are the City of London Police. Their bands are red and white striped, whereas the other forces used to wear dark blue and white stripes. They could be horizontal or vertical, depending on the whim of the chief officer.
They were put on the arm at the start of duty and taken off at the end. This was because for many years, police officers were not allowed to wear 'civvies', having to be in uniform, even when off duty. People saw them with their wives/girlfriends and reported them for the discipline offence of 'idling & gossiping'. That is why the duty band was brought in.
Hope this clears up the query.
If you have a patch or hat to spare, we can find room at the museum to display it. Our addres is on our website, which I hope you will visit.
Yours in friendship,
John Endicott,
Curator.