Crest Pharmacy, who operate the site at the Puregym in the town, said they had plenty of slots for first doses free before the announcement.
They were concerned that the doses may go to waste, due to the high percentage of people aged over 50 that already have had their first dose.
The announcement eliminated those fears, with national demand crashing the NHS booking site this morning.
Now patients who want to have their first dose at the centre in the Ropewalk Shopping centre will have to wait until next week at the earliest.
The gym itself is closed until June while vaccines are given out, but members can visit any other Puregym branch.
You can book a vaccine through the NHS website.