I've been on and managed to book, I'm 61 and it let me.
However it appears that others who have tried booking haven't been sent a reference number and the system has said to 'rebook' their chosen date. I assume it is dependent upon area, centre and the date you pick.....?
As far as I can see, if it lets you book a vaccination, take it; if the system won't let you, you will be called soon enough....