MK has one of the largest vaccination centres in the region at Saxon Court and it also has seven other local vaccination hubs.
But when people have followed the instructions on their letter and tried to book on the NHS website, they have found not a single appointment is available in the borough.
Instead they've been offered jabs at smaller centres in Northampton Luton, Bedford, Aylesbury or even London.
"I tried for ages, but it just said there were no appointments in MK. In the end I booked one for Northampton, where I has a choice of dozens of slots," said one 62-year-old.
"The website then asks you to book your second jab, which is for a date in May, more than two months away. I tried to book that in Milton Keynes but again had no success."
Another couple, booking at the same time, could only get slots 25 miles apart - one in Luton and one in Aylesbury.
One man tried to books a slot repeatedly all yesterday evening and ended up being offered an appointment in North London.
"I wonder if Milton Keynes has a problem with vaccine supply at the moment," he asked. "It all seems very strange."
The Citizen asked the Bedfordshire, Luton and Milton Keynes Clinical Commissioning Groups if there was a problem.
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.”
The CCG confirmed it reviewed the number of appointments it can offer at its vaccination sites based on expected supply of the vaccine at each site.