I've been trying to get a reasonable location for my booster and the availability is awful, just checked the link that was posted and i got Portsmouth as my nearest ! If i go through other nhs back doors the best I get is Brighton or Chi, I really don't understand why you can't get a vaccine in Worthing , its mystifying .
Edit : I get the impression that there are no new vaccination centres opening, just if you turn up at one they HAVE to vaccinate you no matter how many turn up at once.
I had my national NHS invite for the booster a few weeks back. As you say you have to go to either Brighton or Chichester for them.
This morning I had my invite from my GP surgery (Lime Tree) to book with them in Worthing. The first available appointment is the 21st November.