An interesting piece of info in the Badges of Rank files at the National Archives is that there were four different manufacturing options considered for badges in October 1941: Embroidered, Calico Printed, Woven & Screen Printed.
All types were available at the same time. It was a decision to go with embroidered for the first batch but as more and more badges were needed the printed variety was ordered.
Each had merits and demerits - Embroidered looked better and could put up with wear and tear better; CPA (Calico Printers Association) was cheap but frayed. Woven was quick to produce. Screen Printed very fast production but faded.