I push DD in the way that I expect her to work to the best of her abilities but I respect that she chooses the subjects.
She applied to study history from September, her main focus is late mediveal/early modern. She loves it, she thrives in it, she is utterly focused and determined. She sees her future in it, not as a stepping stone to go into finance.
Your DD sounds great @reluctantbrit - hope she achieves what she wants.
We hope to take a similar approach with our (much younger) DD. I feel strongly that there is a middle way between the laissez-faire, 'As long as they're happy' mindset of many Brits and the pushy, tiger parent approach of certain immigrant groups. We want to convey the message that DD is free to choose whatever career path she will find fulfilling, but if it's a non-vocational or niche academic area then she will need to be bloody good at what she does, aim for the top universities etc. Basically that you need to think carefully and have a plan (and a Plan B).
DP and I both attended a super selective grammar school, loved it and did well academically. But that grammar, like many others, is now overwhelmingly Asian and extremely focused on STEM subjects at the expense of everything else (it was much more holistic when we went there, with humanities subjects, music and the Arts afforded equal status). We won't be looking to send DD there, as I want her to have a genuinely holistic education, plus don't want her to face the pressure of intense tutoring, with the bit unlikely outcome that she will 'fail' (there are now around 15 applicants for every place).
On the other hand, I find the attitude of most of our non-immigrant British friends to be pretty non-aspirational and anti-intellectual - there's a lot of obsessing about mental health and 'stress', and essentially the attitude is that you just go to your nearest comp and aim to keep yourself out of trouble. It's not seen as the done thing to be overly serious about academics, or too focused on a specific life goal. These friends are largely middle-class professionals themselves, so I do find the apathy hard to fathom.
The reluctance to be seen to put in effort when it comes to school/academics does seem to be a peculiarly British cultural trait. Even at my grammar there was way more kudos attached to aceing exams without having revised, and everyone pretended they hadn't.