More than 900 people at each site are expected to have been given the recently-approved COVID-19 vaccination by the end of this week.
All patients will have to return for the second dose of the vaccine in approximately three weeks.
The community vaccinations come just a week after the Great Western Hospital in Swindon became the first local venue to offer the vaccine to staff and patients.
Local people are reminded not to attend any of the community vaccination sites, nor their local hospitals or GP practices, without having been invited to do so.
More information about the coronavirus vaccine can be found online at www.nhs.uk