You can be specific about which education discount you want in a retail store. There are three tiers: standard (school), further education, or higher education. I have bought products in Apple stores with these last two tiers, and IIRC the HE discount is around the 20% marker. (NB: If you use HE discount, AppleCare costs ~£50.)
I do remember reading that an unconditional offer letter is fine for getting HE discount. A conditional one isn't, but an unconditional one is. Or if you have the UCAS letter confirming the institution you are going to, that is also fine.