... because the way the web site works makes me think there is a high risk that trying to do so will result in me getting a later appointment.
NHS sent me an SMS overnight inviting me to re-book my second vaccination for an earlier date. But when I follow the procedure, after identifying myself, the only option on the page is to cancel my current scheduled appointment. While "cancel" followed by "book" could logically achieve the objective of changing my appointment date, there's no way I'm pressing a button labelled "cancel" before I have a confirmed offer of a better date.
I've tried the "Book new appointment" route (as opposed to "Manage your appointments") but it leads to exactly the same option, to cancel my existing appointment before proceeding.
It may well be that the "cancel" button doesn't immediately cancel your existing appointment, and allows you to select a replacement date before finalising the transaction, but I have no way of knowing that. Unless someone who has done it can tell me what happens next?
I called the phone number offered as an alternative to on-line booking, but unsurprisingly, they were too busy to talk to me.