The closure of the practice in Folkestone will leave 5,000 people without a GP.
Local health officials have said they will find practices for all patients – but are currently unsure how they will do it.
According to NHS Choices, the practice has been functioning with one GP backed by two other doctors.
Practice manager Christopher Lewis told Kent Online: “The GPs that care for patients at Sandgate Road and Folkestone East surgeries have tried to recruit more doctors to join them to replace doctors who have left or retired.
“Despite advertising for more than a year both nationally and internationally, owing to the national shortage of GPs wanting to join partnerships, no applications have been received.
“There is insufficient medical capacity for the two practices to safely maintain services for the future, therefore they have reluctantly been forced to cease providing services to patients at Folkestone East Family Practice from November.”
After intervention from the town’s former MP Damian Collins, Mr Hunt promised: “If we are back in government after the General Election we will make it a priority to get to the bottom of this.
“General practice in this country is the backbone of our NHS and we will ensure your local GPs have the appropriate resources, and that all of your constituents can count on a good and improving local service.
“We would not allow local people in Folkestone to go without access to this critical service.
“Indeed, as today’s manifesto sets out, we have plans to further improve access to GP services, including at evenings and weekends.”
Earlier this week GP leaders complained there was no sign of doctor numbers increasing – in spite of the last government’s promise to recruit 5,000 extra GPs.
Dr Jonathan Bryant, clinical chair of South Kent Coast Clinical Commissioning Group, has written to patients stating: “We understand this may be an uncertain time for you and that you may have concerns about your future care.
“Please be assured that NHS South Kent Coast CCG is continuing to explore all options to ensure arrangements for your ongoing care and we will continue to update you as information becomes available.”