Watch the full report by ITV Meridian's Kit Bradshaw
Some doctors and community leaders in the South East are describing the vaccination rollout as a "postcode lottery".
While some areas are ahead of schedule, others are still waiting for the first vaccine supplies to be delivered.
This accusation has been dismissed by Prime Minister Boris Johnson.
It comes as people aged over 70 and the most clinically vulnerable are being offered the vaccine from Monday (18th).
people are being given a coronavirus vaccine every minute, across England
One drive-through vaccination centre in Whitstable can give 1,000 coronavirus jabs a day.
Despite being ready to invite more patient groups, the gates have been locked and the vaccinations halted because they have run out.
Dr John Ribchester, GP, says they are worried the vaccines are going to the "new large centres rather than to local GPs".
He said: "GP centres like ours have a desperate need for more vaccines.
"We need to know it's going to come on the appointed day and to move to a situation where we can order it on the day we need it."
Hastings, East Sussex
The lack of vaccines in certain areas is causing concern among those in the initial cohorts who are still waiting to get their jab.
Dee Quinnell, aged 88, is yet to be invited for her first jab.
Her daughter, Jacqueline Rowland, said she's seen a "demise" in her mother's health and said the vaccination would help to "boost her morale and quality of life".
Jacqueline Rowland, Dee's daughter
Headcorn Aerodrome, Ashford
A failure in the supply chain has also been blamed for a number of cancelled appointments on Monday morning at the Headcorn Aerodrome in Kent.
Another vaccination hub is due to open at an airfield in Lydd later this week.
Its isolated location has worried local community groups.
Tony Cooper, Chair, Romney Marsh Breathe Easy Group says he has concerns about the "wiseness" of the decision.
He said: "Elderly, vulnerable and disabled people are being expected to use public transport to get to a desolate bus stop in the middle of the Romney Marsh, when those services for the vaccinations should and could have been delivered by the local chemists."
With reports of some GP practices being deluged with thousands of calls a day.
Those running the vaccination rollout in the South East are urging the public to be patient, and wait to be contacted.
Nadhim Zahawi MP, Vaccines Minister, said those aged over 80 who have not received the letter yet, "remain the priority".
Nadhim Zahawi MP, Vaccines Minister