This is how it works.
There are a group of eligible people.
For arguments sake let's say a million.
They are all eligible. No one person within the group is 'more' eligible.
The patients are spread across (for example) ten thousand surgeries.
That means that each surgery works down a list of a hundred people to book them in.
If like me, you have used the link provided and as an eligible person you were able to book an appointment at a hub. You would be offered one where there was a space. Based on 'soonest ' . So this means I was offered one the day after I booked - but not locally. This was fine for me as I drive and have no issue driving 21 miles to get vaccinated in a slot that was not booked.
Obviously- the number of people eligible is not evenly spread across all Surgeries. Therefore the place I got an immediate slot had obviously offered all their eligible people already. That slot would of remained empty. Had I not used it.
The day after booking , I was offered a slot at a local hub for 5 days time. I was able to say that I already had a slot for that day and another hub. The caller thanked me. Made a note of where I was having the jab and could then add another person to her call list. Giving someone a chance for a jab - who may not have been called until next week.
The system works well and makes efficient use of available slots. Minimising wasted time.