https://deriv.nls.uk/dcn23/8994/89941410.23.pdf
K&K definitely have mis-identified the St Ignatius JTC badge - it's not the school cadet badge from that period as the school did not have a JTC in 1947 either. I think it is another Catholic School cap badge and not military.
Having looked at the back of the K&K badge it is clear to me that the 4 ring fixings are those of a school uniform cap badge and not a cadet badge. They would not big enough for a khaki cap, side cap or beret and are clearly designed for a thin cloth school cap.
The school's uniform badge (currently worn on the blazer pocket) is the green/yellow striped badge without the helm. The badge with the helm is the school crest.