Gents,
With the measurements given, both are cap badges. With pointed serifs on the '2' they are either Hemsley or Inglis. The collar badge measures 31mm x 29mm.
Attached are a few of the variations I have of this unit in my small collection.
The top row shows a maker marked Inglis cap badge and a non-maker marked (pointed serif) collar.
The bottom row shows a non-maker marked (blunt serif) Tiptaft cap and a voided (unknown) cap, the numbers '12' being sweated onto 2 bars.
Apologies for the photo, but that isn't my forte