I also think that bronze badges were introduced for the service dress cap in 1902. If you are interested in WW II officer uniforms, the 1934 dress regulations are the most relevant. They stipulate two bronze buttons for the cap, service dress, soft pattern (which was to be worn on active service and manoeuvres). Line infantry regiments wore bronze badges, the Foot Guards wore (and still wear) shiny ones (Grenadiers and Welsh in gold embroidery, Coldstream, Scots and Irish small but elaborate silver and enamel stars).
As Tony pointed out, the bronze badges disappeared at some point after the war, most likely in the 50’s and certainly by the time the “brigade” cap badges were introduced.
Pre- and early-war caps had, in the belief of collectors, narrower chinstraps than later ones (although I am not sure that is a general rule - the Scots Guards cap in the picture is post-war, made by royal appointment to HM the Queen and with brass Queen’s Crown buttons). I have put together a number of service dress caps from my collection for a quick photo to show differences. The one from the Buffs is particularly interesting as it is the only issued from ordnance stores and clearly dated 1945 - with a very wide chinstrap.
Hope this helps
Robert
Detail of the Buffs cap
And here is a cavalry cap, made from a very different material and with plain, domed brass buttons:
The Gloucesters cap in the first picture is also from the 1950s, but still with a bronze badge, that is why I included it. The material of that badge is very different from earlier bronze or painted brown badges and a bit too shiny for the original purpose of camouflage.