I have done some limited research into this badge and have not been able to prove the claim that it was a Cadet badge but it is a badge with links to this organisation:
http://www.coopers-hall.co.uk/history
It was definately not an OTC badge as the school did not posess an OTC no matter what any well known auctioneer may claim. The Cooper's company does have a link to Surrey ACF but again this is not an ACF badge.
The Coopers' Company and Coborn School had a cadet corps and they were part of the 2nd City of London Cadet bn. The London Cadet battalion were affiliated to the London Rifle Brigade. This information taken is from a 1916 school magazine which records the cadet corps new affiliation in that year.
As a follow up Bosleys sold this s/t and dated it from 1911-16.
https://www.the-saleroom.com/en-gb/a...2-a862010bad07
they too stated that it was absorbed into the 2nd Bn in 1916.