Cambridgeshire Community Services NHS Trust, which runs the large sites, said the number of appointments offered was "partly based on the expected availability of vaccine".
Addressing concerns over a lack of vaccine availability in Norfolk, the trust said new slots were added on a frequent basis.
A spokesman said: "Anyone in a priority group invited to have their vaccine can look for an appointment at a time and location that’s convenient to them through the national booking service.
"New appointments are regularly added to the system as they become available, and alternatively, people can choose to wait to be contacted by their local GP services."