I went through the state and private, both schools used CP, the state school more than private, but an unfair comparison as it was co-ed. The private sector had much higher expectations of its pupils and maintained a far higher level of discipline. This was 1960s an era when both types of schools commanded respect, you stood for a teacher entering a room, spoke when spoken to, foul language unheard, and were punished for breaking silly rules.
Once CP was abolished state schools, the majority of private schools followed practice, a few hung out for a further ten years, based on tradition rather than actual need. State schools which mainly relied on cane wavering as a main deterrent saw nothing replace it, whereas, private schools still had a good system of rigid alternative punishments to fall back on, based on loss of privilege,