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Minster Medical Group is to take over the GP walk-in service at Sheppey Community Hospital. It will replace DMC Healthcare from Monday.
The switch has been ordered by NHS Kent and Medway Clinical Commissioning Group (CCG) which plans and pays for the county's healthcare.
The new service will be open from 9am to 9pm, seven days a week, and now coincides with the same times as the hospital's minor injury unit.
The MIU will continue to be run by Kent Community Health NHS Foundation Trust.
DMC has not had its contract to run a GP service at the hospital renewed after 12 years either in the health shake-up despite the Care Quality Commission rating it as Good. In September, 9,000 patients were told they had to sign on with other doctors.
DMC has five doctors, one paramedic, four nurses, a pharmacist and a support staff of 13 at the hospital, according to its website.
In July, last year DMC announced it was to hand back contracts for key services in Medway and other parts of the county. The south London-based company was previously stripped of contracts to run five GP surgeries in Medway.
A former nurse at the centre said: "I was there six years and for that whole time it was always rated good. Personally, I think the CCG has a vendetta against DMC. DMC took on the Medway practices when they were already failing. It takes time to turn a surgery around - time which wasn't given.
"I don't think the new service will be any better."
She added: "It's shame because as a team we were a real family and it was enjoyable to go to work. We are all so sad and upset we had to leave and break up our team.
"We are all so incredibly angry with the CCG as what it has done doesn't make sense."
Both DMC and the CCG have been asked to comment.
Patients can use the new service by walking in or booking a 15-minute appointment using the 24-hour NHS 111 phone line. The walk-in service is for urgent health conditions that a GP would normally treat and diagnose such as ear, throat or skin infections and minor illness.
Minster Medical Group is a partnership of GPs who already provide services at two sites on the Island including an existing surgery at the hospital in Plover Road, Minster.
The minor injury unit is for more serious problems such as suspected broken bones, sprains and strains, animal and insect bites.
Staff can treat cuts, skin infections, allergic reactions, asthma attacks and can remove foreign bodies from eyes, ears and noses as well as splinters and fish hooks.
They can tackle burns and treat head injuries if there has been no loss of consciousness.
The hospital's X-ray department is open Monday to Friday from 9am to 5pm, except for bank holidays.
The CCG says it is planning to upgrade the hospital to an urgent treatment centre in the "coming months".
Urgent treatment centres are new GP-led units open at least 12 hours a day, every day, and offer appointments which can be booked through NHS 111 or a GP.
They have equipment to diagnose and deal with many common problems normally dealt with at A&E and are part of the Government's action to ease pressure on acute hospitals to free them to treat the most serious cases.