A lot of people have the same issue, but don't worry, you don't actually need to add your bank details in order to submit your application. You'll probably have the option of saying something along the lines of 'I can't give my bank details at this time', and then simply adding your details later, once you open a student bank account. If you do end up having to add an account (I applied via SFW, so it may be different in England), you can still change your bank details up until I think a week before your first payment, so you have plenty of time to sort it out.
Plus, most banks will only let you open a student account after results day anyway, so student finance won't really expect you to have it sorted at the time you apply