Just talking from the pov of the lower income areas and their schools for outreach.
There always seem to be a couple from these schools who go into careers in science, engineering, etc.
I'm sure there would be more to reach.
However, I remain convinced its a preserve for those who are strongly encouraged by parents, not necessarily employed in these fields themselves, but at least educated in their worth.
Paul Nurse came from a working class background and said he found Science more accessible than the Humanities at his grammar school because parental input made less of a difference. The Humanities required cultural knowledge that the middle middle class prize. Historically science was more of an even field. Admittedly, if my and my friends are anything to go by, that is no longer true. I'm a biologist working in the pharmaceutical industry and all my friends force feed their children science (as well as theatre/travel/museums/art galleries). We all know it's a good career that is family friendly (for both parents). But at work there is a real mix of social backgrounds, I'm in the NE and a lot of my colleagues were bright kids from stable working class backgrounds, as well as there being a fair smattering of posher folk from all over. I suspect if I went to e.g. an art gallery there would be less of a social mix.
I think women are breaking into STEM subject but physics is the last bastion of male domination in English speaking countries. I'm actually really happy that so many women do maths (40% is high enough that stereotype threat won't apply anymore), I think that is a more useful general subject to study and there would be very few careers that would demand a physics degree but not be happy with a maths degree.
But agree that A levels force specialisation too early, I did Highers in Scotland, I had 7 Highers, all the classic sciences and a few humanities as well, all the bright kids at school would have done a similar mix, we all HAD to do English and Maths at Higher, and at least one Science. And because we do 4 year degrees you are admitted to a faculty rather than a specific degree course so I didn't actually choose my final degree subject until the end of my second year at Uni. I think that flexibility is great and allows you to make a choice based on some real knowledge of the subject as a adult (I made my final degree choice at the age of 20 and the choice between Science and Humanities at 18).