As an ex-soldier, this topic has long been fascinating to me. One thing that never appeared on my uniform was a trade badge. On number 2 dress, there were stripes (or not) indicating rank., with the Corps badge (Mercury aka Jimmy for Royal Signals) and, if applicable, medal ribbons on the left breast, all topped off by the Royal Signals blue lanyard on the left shoulder. (Had to be left side to distinguish us from Royal Engineers). Combat kit bore only rank stripes and working dress had the same, rank stripes and nothing else. There were no trade badges. If someone turned up in my workshop and saw me repairing a radio, they would recognise immediately that I was one of the various radio technician trades. In addition, there sometimes Divisional Flashes. If you were posted to a unit with,for example, 7Div, you would end up wearing the Desert Rat flash on the upper arm. Generally, when anything 'different' was happening, the dress would be laid out in Orders. I think we were proud that we understood the definition of "uniform".
And then we used to gaze upon our colleagues in the R.N. and R.A.F., wondering what all the badges were about. And when it came to pilots (drivers, air frame) the whole thing took on a circus like appearance, with big round, gaily coloured circular cloth badges adorning the flying suit.