Just found this and can't resist adding my two penneth.
I went to a very bog standard northern comp where extra curricular activities were non existent. My parents left school at 14 and were clueless about academia so I had no advice from them. I got all As at GCSE and applied to Cambridge after getting AAA at A level. I originally applied to a decent RG uni and was all set to go but when I got my results I changed my mind about my subject and decided to give Cambridge a go.
There was an admissions test for my subject for which I did no prep at all. Hadn't even seen a practice paper. No prep for interview either. I had left home at 17 and was working in London so just took a day off work for the interview.
I found the interviews (subject and general admissions tutor) quite enjoyable. It felt like a chat. Maybe they gave me a break because of my background but in hindsight I think I probably came across as very independent (and in no way pampered!).
My dh went to the same college but went to private school, did practice tests, interview coaching, had graduate parents etc. I have no idea how I got in really but I am so glad I did.
It was very tough academically. I got a 2.1 (1sts in some exams). Have since done other degrees and post grad at other good unis and found it easier to get 1sts there than my Cambridge 2.1. Not because I was an experienced student but because the workload was lighter and the standard required for good marks not as high.
Socially I found Cambridge very intense and weird at first. People from posh schools slotted straight into the drinking societies and boat clubs and at first I thought I'd made a big mistake. However the standards are so high, supervisions so intense, the competition so fierce as everyone is very bright, that i think it fundamentally changed the way i think and work. Sure this might have happened elsewhere but, having studied elsewhere, I'm not so sure. I also made great lifelong friends, met my dh and have found it has opened doors for me for my whole life.
That said I did have a pretty big psychological wobble in my final year due to the academic pressure. I appreciate that other students face massive pressures in other ways but anyone thinking of Cambridge should be aware that it can feel like an academic pressure cooker at times.
I would advise your daughter to give an application a go if she's interested. It sounds like you'd be a good person to catch her if she doesn't get in.