Thousands of letters were sent out to people in Shropshire, causing confusion and anxiety as over 80s were invited to appointments in Birmingham, Manchester, Bristol and other parts of England.
It coincided with the announcement of seven mass vaccination centres opening throughout England.
David Evans, joint accountable officer for Shropshire, Telford & Wrekin Clinical Commissioning Groups, said the larger centres provide an additional option to local sites, and people will still be able to receive a jab closer to home if they prefer.
He said: “Some eligible local people have received letters over the weekend offering them the opportunity to book an appointment at one of the new centres.
"They can of course take up the offer, but we want to reassure everyone that they can still choose to receive their vaccination closer to home and do not need to travel out of the county unless they wish to.”
People are being asked to wait to be invited to book their vaccination and should not contact their GP or turn up without an appointment.
Several sites are already delivering vaccinations across Shropshire.
They include the hospital hubs at Royal Shrewsbury Hospital and Robert Jones & Agnes Hunt Orthopaedic Hospital in Gobowen, as well as local vaccination sites at Bridgnorth and Malinslee, Telford.
Health chiefs say the vaccine will be offered to more people and at other locations in the county as soon as possible.
These will include further local vaccine services provided by GPs and pharmacists, in people’s homes for those who are housebound and new dedicated vaccination centres.
It is expected that Telford International Centre will be operational as a mass vaccination centre by the end of the month, though health bosses are yet to make an official announcement.
Nationally, more than 600,000 eligible people will receive letters inviting them to book an appointment at one of the mass vaccination hubs in the next week.
This includes some local residents who have yet to receive their first dose of the vaccine, who are aged 80 and over and who have a postcode that indicates they live within 45 minutes of a centre.
The first seven mass vaccination centres to open around the country include Millennium Point in Birmingham, Etihad Tennis Club in Manchester and Ashton Gate in Bristol.
People who have received a jab since the letter was sent out or would prefer to wait to be invited to attend a hospital or GP service, or they already have an appointment booked with their GP, can simply ignore it.
Those who book into a vaccination centre will be greeted by volunteers who will marshal car parks and register them when they arrive.
Bookings are staggered to allow social distancing.
They will receive a health status check and a pre-vaccination assessment before they receive their vaccine from a trained vaccinator, and then be observed for 15 minutes. The process should take under an hour.
Health Secretary Matt Hancock said: “Through our vaccine delivery plan we have already provided a first dose to more than 1.2 million people in England and we are mobilising the government, NHS and the armed forces as part of a massive national effort.
“The vaccination centres are an important milestone and will help accelerate the roll-out further.
“They will work hand in hand with GPs, pharmacies, hospitals and care homes to offer vaccines to everyone in the top four priority cohorts, saving thousands of lives and helping us start to return to normal in the future.”