No, teaching and nursing weren't considered menial occupations. They were the pinnacle to which girls (in England and Wales)could aspire. Another route was working for the GPO. There was a career path for employees. They took exams, which were published in the London Gazette. Girls in big cities could become secretaries, but few of them became doctors, senior managers, accountants,lawyers,etc.
JessM Before the 1944 Education Act was enacted in 1947, there were grammar schools, which had exam entrance, but they weren't free, unless the pupil won a scholarship. Both my parents passed the entrance exam. My Mum won a scholarship, but my father didn't, so his parents had to pay. Wealthier parents of bright but not outstanding children objected to the 1944 Act, because their children were pushed out of grammar school places. The choice was a secondary modern or private school. It was these parents, who later pushed for comprehensive schools. One of the very first comprehensives was in Anglesey.