After your offer is made unconditional (which for most people is after A-level results day) and you have a letter to say so. Most banks won't open a student bank account for you unless you have that letter.
Basically what the person above said. Generally your current bank account can be changed into one, you don't have to 'create' a new one if you don't want.
I'm with the Natwest and they recently sent me a letter saying how my account will change (no more interest, free student railcard, interest-free overdraft etc) - you should probably get something similar from your bank?