Dr Sarah Raistrick, from Coventry and Rugby Clinical Commission group (CCG), said people did not have to travel to the centres but admitted the letter did not make that clear.
“You can wait and be contacted by your local GP service and have it locally if you’d prefer.
“If you sit tight, you will be contacted and I’m hopeful that if you’re 80 or over, by the end of this month you will have had your vaccination whether that is locally or whether you have chosen to travel,” she said.
Work will be done with the NHS locally and nationally to make that message clearer, she added.
The seven centres were chosen to give a geographical spread covering as many people as possible and are capable of delivering thousands of jabs per week, NHS England has said.