This one is maker marked Fattorini Hockley St. Birmingham so according to the firm's history dates between 1919 and 1928. Whether it is an OTC badge or not is unclear but with a vertical shank it is for a peaked cap rather than a boy's school uniform cap.
https://www.gracesguide.co.uk/Fattorini_and_Sons
1919 Thomas Fattorini (Birmingham) Ltd was established at Trafalgar Works, 5 Hockley St., Birmingham to serve the business for medals and trophies of Skipton jewellery shops.
1928 the name of the Birmingham business was changed to Thomas Fattorini Ltd (Regent Street Works, Birmingham).