A message posted into a community Whatsapp group chat claimed that space had been made available for 'hundreds' of people to get the jab.
The message was shared far and wide and eager people from as far as Hove and Farnham were calling Midhurst Pharmacy and the town council offices in hope of getting the jab.
These claims have since been dismissed as false.
The message read: "Hi folks, a member of our church runs the Midhurst Vaccination Clinic and due to scheduling issues, they have space for hundreds of people to be vaccinated today (Monday, March 22). If you know *anyone* who is over the age of 40, not yet vaccinated, able to travel to Midhurst between 2pm - 4.30pm today."
The message later added: "Please share this as far and wide as you possibly can to avoid these vaccines going to waste."
Midhurst Town Council highlighted the issue in a post to social media and told residents not to attend the vaccination site unless invited.
A spokesman said: "Oh no! Some false information is doing the rounds!
"We have been alerted to a post going round on group chats and social media about extra vaccines being available at the Midhurst Memorial Hall today.
"We have spoken to the Midhurst Pharmacy who are running the vaccination programme and they politely request that unless you have been expressly invited for your vaccination today to not show up at the centre as you will be turned away."