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Dover district's second public vaccination centre expects to inoculate more than 1,200 by the end of the week.
And medical staff have begun jabs for residents in their own care homes.
The Clockwork Pharmacy in Deal High Street began its jabs last Saturday.
The work is being done with volunteer nurses and extra pharmacists and patients are injected by invitation from health officials only.
Clinical lead Nickil Patel told Kent Online: "The programme has got off to a flying start with well over 1,200 patients due to be vaccinated by the end of this week.
" It has been a truly wonderful and humbling experience - with countless messages of support, gratitude and even relief from the many patients we've had the pleasure to vaccinate.
"The team at Clockwork are working tirelessly to ensure patients are vaccinated safely and promptly.
"We are also liaising closely with the NHS to increase capacity in order to better serve the community in Deal. Thank you to everyone for your continued support and well wishes."
The new centre for Covid-19 jabs for the public opened after a campaign by locals to have one in the town,
Until then there was only Dover Health Centre in Maison Dieu Road, which began inoculations on January 15.
The one at Aylesham Health Centre is for health and care staff only.
Health authorities had said the programme would be expanded locally.
Balmoral Surgery in Deal is also expected to start vaccinations but it is not known when yet.
Meanwhile all older people living in care homes in Dover and Deal have now been offered visits for vaccination.
All this is part of the biggest inoculation programme in British history as the Government speeds up its Vaccines Delivery Plan.
The aim is to protect the top priority groups, the elderly and medically vulnerable, by mid-February.
Natalie Elphicke, MP for Dover and Deal said:“I pay tribute to the hard work of our local GP surgeries, nurses and care home staff.
“I will continue to press hard to make sure our older and vulnerable residents receive this life-saving vaccine urgently.”
New vaccine sites were agreed following a campaign led by councillors Susan Carlyle, Pam Brivio, also secretary of the Dover Senior Citizens Forum, and voluntary worker Terry Bishop.
They did this after it became apparent that vulnerable groups, many of them elderly, did not want to risk travelling to Dover.
Mrs Elphicke had also pressed health bosses for new sites in the Deal and Walmer area.
Priority groups in Sandwich are being offered appointments in Broadstairs and by last Wednesday more than 900 from there were injected.
Read more: All the latest news from Deal