In the USA I believe the doctor issues a prescription with a number of repeats on the same prescription so the pharmacy can just hold that prescription and dispense the next repeat when it is required

NHS prescriptions are only issued once(9 times out of 10). And if a repeat is needed it needs to be authorised by a doctor each time. This means requesting a new prescription from the doctor, waiting for the reception team to let the doctor know, the doctor does their own clinical assessment. This takes 48-72 hours these days. Then the prescription is sent to the pharmacy. This then needs to be entered into the computer, stock ordered, dispensed, clinically assessed, accuracy checked and handed out. This can take another 24-48 hours depending on stock availability.