This is some stuff that helped me with my Prelims assessment which was an essay in class.
In reference to English, I suppose when you're ready to start doing practice essays/drafts, so when you've thoroughly went through your Mod A texts and you have an in depth understanding of the themes, contexts, characters, purpose etc.., by that time you'll naturally know most of the quotes you need to since you would've went through the texts quite a bit.
If you still can't remember a quote, I would just try using flashcards or something similar to the sort. Its better to memorise more shorter quotes that work well without requiring much context, you can remove unnecessary lines to get to the point through ... e.g Richard III's opening solilioquoy" since I cannot prove a lover... I am determined to prove a villain".
My quotes aren't that long anyways so its not too hard to remember, its easy to remember them by thinking of the scene. So e.g for that quote I listed, I would try to remember the opening soliloquy from a stage play and think how Richard felt at the time., where was he... then it becomes more easy. Not sure if I formulated that right but that's how I remember most of my quotes.