What is wrong with going to A&E for an (as you said yourself) emergency?
A pharmacist dispenses medications and should know about their safe usage. They won't tell you how to bandage a wound.
Going to A&E and waiting there also means you're losing 4 to 6 hours.
111 you just get some robot asking you a never-ending list of inane questions before someone tells you to either self-care at home or go to A&E.
A pharmacist should be able to administer the supplies they sell, particularly wound dressing and care. It's a requirement in some other European countries like France (where pharmacists are doctors), but in the UK the reality is that most are unable to do so.
If it was in hours, I'm surprised they didn't get a nurse appointment for the cut.
Pharmacies provide much more than just medicine.