Those over 70 who live in Milton Keynes are urged to either book their appointment online or by calling 119 free of charge between 7 am till 11 pm seven days a week.
Appointments can be booked online through this link.
Those without internet access or who may not feel comfortable online can call 119 free of charge between 7 am till 11 pm seven days a week.
The age group is particularly important to reach given 83% of all people who have died with coronavirus are over 70.
Health Secretary Matt Hancock announced the policy is changing to make sure no-one falls through the cracks as the drive to inoculate against COVID-19 continues.
He also urged everyone to check in with grandparents, relatives and friends who are over 70 years old to make sure they book an appointment "as soon as possible, so they can be protected against this awful virus".
It comes as the race intensifies for all those in the top four priority groups to get their first jab by 15 February before attention turns to rolling the vaccine out to the remaining five groups, reaching all over-50s by May.
Another 333 people were also reported to have died within 28 days of testing positive for coronavirus on Monday, taking the total since the pandemic began to 112,798.
Previously, people were told not to get in touch with the NHS to ask for a vaccine appointment and instead wait until they were contacted to avoid overwhelming the health service.
However, they are now being urged to book their own appointments to ensure no one is missed.
So far, more than 12 million people have had their first coronavirus vaccine and 512,581 who have had their second dose.
