Happy New Year!
Were they ever a real thing or just the stuff of fantasy? There are enough references out there to believe that, although it was unusual, very occasionally a teacher did smack an errant pupil with the flat of his/her hand across their bottom (and I witnessed that on more than one occasion). And it is also beyond dispute that in the case of really bad behaviour, a pupil might be sent to the headmaster's office (or that of another senior member of staff), and punished with a strap or cane. In the later years before the abolition of corporal punishment in UK schools there was a move towards such punishments, especially for girls, being given on their hands rather than their bottoms but that hadn't always been the way. It is also a fact that some pupils getting the cane or strap would brag to their peers about it afterwards and feign indifference. I rather doubt that anyone would brag to their peers if the headmaster had put them over his lap and spanked them. They might have left his office with a very sore bottom, maybe crying, but desperate for their friends not to know they've been given a punishment more associated with small children.