The truth of the matter is that there is no historical basis to the Beadle as depicted by Sondheim in Sweeney. Beadle Bamford owes more to a invention of Lionel Bart’s in Oliver! than historical fact.
A Beadle was a lay official of a church, synagogue or educational establishment who ushered, kept order, made reports, and assisted in various functions. A Beadle was also a minor official who carried out various civil, educational, or ceremonial duties.
Unlike Timothy Spall in the film, Beadles had a specific costume that they universally wore which included a bicorn hat worn side-to-side (‘athwarts’) and a tabard with decorative shoulder pieces. He always carried a staff of office.
The nearest to the Sweeney version of a Beadle is a uniformed security guard such as still found at the Burlington Arcade, an upmarket shopping mall in Piccadilly, London.