Under Consumer Rights Act within 6 months, it’s presumed faulty and they have to replace or repair, your choice. Though they can argue repair if it’s cheaper.
Everything else you’ve said is correct but this isn’t quite right. You can state a choice of course, but the retailer is under no obligation to honour that choice. They just have to rectify the fault without significant inconvenience to the customer.
As you say, the contract of sale is with the retailer and it’s their responsibility, not Apple’s, to resolve the issue. However as others have said, Apple being Apple the OP will probably get a swifter resolution dealing direct with them as their customer service is excellent (doubly so given that the retailer is Currys).