No reference letter, universities don’t want to see them. You don’t need work experience for a PS you can easily talk about other things like reading, law related super-curriculars as already mentioned. I was lucky to apply for and get on two schemes (without having any inside contacts), but many don’t manage it in sixth form and some students who do get them, it can be because mum or dad of someone works there, so it’s not seen as mandatory or make or break.