I have a far closer match for your badge here:
http://www.loyola.essex.sch.uk/
It's another Jesuit School in UK but as a preparatory school would not have had a cadet unit.
The Loyala prep colours are red and gold from the Onaz family: originally seven red bars on a field of gold, represented the seven heroic brothers of the Onaz family who distinguished themselves in battle.
The combination of the Loyola and Onaz family bearings can be found on seals of Jesuit schools around the world. Ignatius Loyola being the founder of the Society of Jesus (Jesuits).
Where as the St Ignatius green bars over a gold background come from I am not yet sure.