In my life I've been dirt poor (as a kid), average income (working overseas but tax free so standard of living was very comfortable), and "ordinarily poor" (now) after a stint of "dirt poor" in between those last two (due to illness).
I think it's very, very difficult for people who've always been very comfortable, and who have no idea whatsoever that even their circumstances may one day change, to have any concept of how hard it is if you've always had to worry about money. One thing they don't understand is how hard it is to cope with the concept of borrowing huge sums of money for an education that might or might not have a decent ROI at the end of it. There is always the fear that you might not be able to pay that money back.
I would not have been able to do any of the educational courses I did without a full grant (uni/teaching) and support from my employer (course fees and time off to study). My sense of being socially and financially inferior to everyone around me has never left me and never will. I was one of the lucky ones, though. I had fabulous teachers at school, especially in 6th form, and since very few kids stayed on at 6th form in my school, effectively we had small group/individual tutoring. At home, to put this into context, while my parents were in favour of education, The Guardian and The Times were regarded as terribly snooty and high brow, and the paper my dad "read" was the Sun. Going to uni was a HUGE culture shock, not least because I encountered lots of people from the same background as it sounds like your DD's friend comes from. In the years since I've met people from a range of backgrounds, from very wealthy old money to homeless on the street without a penny to their name. I've met many people who started with God knows how many advantages in life who've made an utter mess of things, and as many more who started with nothing and have managed to carve out a reasonable life for themselves.
Depending on where you live, there may be bursaries and support available to help your DD, but to be blunt, when you're as poor as I was growing up, you either assume they're not for you or you never hear about them in the first place. University is for rich kids is the perception (and £27k for tuition fees alone might be peanuts to some people but it's more than a year's salary to look after a home and family for many others). I've studied at 3 universities, been employed by 1 more, and had "Honorary" status at a 5th. At 3 of those universities the students, and the lecturers, were primarily from what marketing/market research folk call the AB social categories, with a smattering of C1 and the very, very occasional D. The other 2 unis were very different; one was a former poly, so you could do a course and come out employable without having to do another year of study; and one was in a particular part of the UK where state education is generally very good indeed and students usually stay at home or at least within the province to study.
With regards to tutoring, it might be worth looking into the charity intouniversity.org which I only found out about recently. Once upon a time the OU would have been an option, or part-time study, but these days they're just as extortionate as the mainstream universities. I also don't know if it might be of interest, and heaven knows how Brexit is going to affect things, but there are some universities in Europe which offer free/funded university courses, some of which are taught in English. A friend is studying an MA that is funded (she has to pay for the study schools, of which there have been two, one per year).
I think we're way too hung up on degrees as a measure of intelligence and worth in the UK (and I say that as someone who has studied A LOT). Unfortunately even now many teachers go straight into teaching from university so it doesn't even cross their mind there are alternative paths out there.
There are other options, like apprenticeships, or vocational qualifications. My sister doesn't have a degree; she started on what was then one of the Modern Apprentice Schemes, got her basic set of qualifications to NVQ 4 in a profession; and her company has paid, over the years, for her to take more professional qualifications. She definitely earns more than I do, for all the pieces of academic wallpaper I've collected! Plus she was happier in her job which is much more important.
Some of the "milkround" recruiters like the Accounting Firms also take 'A' level students as employees, and again, train them up over the years. I also know of people who had their degrees funded by the Armed Forces. So full-time university is not the only option...