…a children’s book from late 50s early 60s (I suppose it could have been made earlier or at least the story could have been set in previous decades) about a little boy who wore calipers; he searched for conkers and his clothes were warmed by the fire. He may have had a nanny?  He may make toast on the fire with his mum/nanny?  I would say it was quintessentially English but maybe just middle class?