If you go to in to a Sainsbury's and that store has plates upon plates of pre-sliced meat, that store is doing it wrong. They are supposed to display whole joints, cutting slices to the customer's specification. They can pre-slice, but generally it should only be done on special offers (or other fast selling lines) because the product sells fast enough to limit deterioration. If they try to give you some that's already sliced then just ask them to cut some instead - they certainly shouldn't refuse.
I don't know about other retailers, but if I ever went to a deli and got told 'no' when asking for meat to be sliced fresh, I'd be having a word with the manager. There's no reason for refusing.