In addition, the take-up of the vaccine among over-50s in the Newport/Central primary care network (PCN) has been better than average, said a senior PCN doctor.
About 15,000 over-50s have been given coronavirus vaccinations at Audley Court, the Combat Stress site which was chosen to host Newport/Central's dedicated vaccine hub.
The PCN covers the town's Wellington Road and Linden Hall surgeries, as well as medical centres in Donnington and Shawbirch on the northern fringes of Telford.
"Altogether we found it was a really successful operation," said Dr Stefan Waldendorf, clinical director of the PCN.
"We have gone through a huge number of vaccinations in a short period of time.
"I think we've had a very good uptake. I don't know the exact figures but across the PCNs here we are higher than average."
Audley Court caters for over-50s and now that most people in the relevant cohorts have been given their first doses, staff there have been inviting back patients for their important second jabs.
Dr Waldendorf said it was important for patients who have had their first dose at Audley Court to make sure their second is also given there, because deliveries of the vaccines are dependent on the amount of people given their first jabs there, and disparities could result in shortages or surpluses.
"It depends on the vaccine deliveries – at the moment we're open most days because we were busy in the first few weeks.
"I think it works exceedingly well, we have had very, very good feedback from patients, the staff who work there and volunteers.
"People should go back to where they had their first doses. They should ring their surgery if they get an invite and they can't make it.
"The message would be: 'wait for an invite from your surgery and let them know if you can't make it'."
People waiting for their first or second appointments are advised to be patient until they receive a text message inviting them, or a phone call if they do not have access to a mobile phone.