Cosette,
I think a lot depended on costs and whether the family could really afford it. There was also a tendency in some families for it to be assumed that girls would get married at an early age and hence the whole process would be a waste of time & money. Bear in mind that people get married much latter today, if at all. I passed and went to Moseley Grammar, but my father died two years later and my mother, doing three part-time jobs to make end meet, could not afford for me to stay to do A Levels. That suited me because I hated school and couldn't wait to leave - a mixture of poor eyesight, bullying and not being allowed to do the subjects that I wanted to and that I was good at. A lot of thopse problems are still there nearly 70 years later, and given the lack of discipline, I cannot see some of them being solved in the next 70 years.
Needless to say, my full-time education did not resume until I was 43 years old and financially able to do an HND, in which I got a Distinction, before the onset of charging to do higher education courses. Today even that option would not have been open to me.
Maurice