ablertschoice, my own DD went from a state primary to a selective, private girls' school in London. The first 6 weeks were a shock.
At her state primary she had very little homework. When she did get homework, she made a real meal of it, doing it to absolute perfection.
This mind set, coupled with nightly homework made life difficult the first term. Additionally, she had two MFL and Latin which involve quite of bit of rote memorisation, something she was never asked to do at her state primary aside from learning her times tables.
To get her over this challenge, we gave her a LOT of support till the October half term. Every night we asked her what homework she had and when it was due. I sat with her and helped her memorise vocabulary words for all three language classes. I showed her how it is done and did with her. Luckily I am fluent in French and Spanish and could help her ear adjust to the sounds. Being from a state primary, the majority of kids being from prep schools were ahead of her in Latin and French which dented her confidence. When she had open ended projects (essays, drawing, making things) we assured her when things were "good enough" and encouraged her to consider things finished and to stop.
After the October break, she no longer wanted my help with languages (I was pretty sick of language homework 4 nights a week myself, after all, I wasn't in school!) She also now realised when things were "good enough" and it was time to move on. I still asked what homework she had, when it was due, and what her game plan was for getting everything in on time.
After Christmas, we just left her to it, unless she came to us on the odd occasion asking for help.
By year 8, we have butted out entirely.
I suppose some people might criticise that we were "helicopter parenting" and think it was a bit weak to support her like that. But, I think all kids need parents to help them with the "soft skills." In DD's case, it was a new and radically different environment that she was not prepared for by her state primary. So, we model the behaviour and strategies that she would need to flourish and held her hand until she was ready. Looking back, it only took 4 months of involvement from us, and now she is confident in her ability to manage herself.