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An MP says health bosses should be "waving a big stick at surgeries not delivering the goods".
Kelly Tolhurst was speaking this week following concerns about under-pressure Thorndike Medical Centre in Rochester.
As previously reported, many patients have complained about having to make "hundreds" of calls to get through for an appointment as the line is "always engaged".
One mum told KentOnline how after failing to reach reception, she took her daughter to A&E at Medway Maritime Hospital.
Borstal resident Andrea Waite says she called more than 100 times after becoming concerned about an abnormal swelling on eight-year-old Milly's leg.
An X-ray later revealed a genetic bone condition and she is now awaiting an MRI scan.
Rochester and Strood MP Ms Tolhurst says she is demanding answers from the Kent and Medway Clinical Commissioning Group (CCG), which oversees local practices.
She said: "It's not just the Thorndike, there are other surgeries having problems. But there were problems with the Thorndike way before the pandemic."
She said communications had worsened during lockdown with the increase in advice being given over the phone instead of face-to-face meetings.
She said: "Some surgeries have reacted brilliantly and others have not.
"The CCG should be waving a big stick at surgeries not delivering the goods and tell us how they need help. I have asked for information and answers and will be keeping up the pressure."
Meanwhile, national healthcare regulator the Care Quality Commission has confirmed it has been contacted.
Its head of inspection for primary medical services, Neil Cox, said: “We are aware patients have had some issues with accessing Thorndike Surgery.
"We are regularly monitoring all registered healthcare providers in the area and carrying out inspections where needed.
"We are also in regular contact with the CCG and NHS England regarding all current and evolving risks in the area and will consider regulatory action should this be necessary."
When asked whether an inspection was likely, he said: “As these are normally unannounced, it would be inappropriate to comment further.”
The CCG did not directly respond to specific questions about Thorndike.
But its clinical chairman, Dr Navin Kumta, previously blamed a rise in demand and the fact local surgeries' staff had been helping with the Covid vaccine rollout.
He said: “This means local practices are working harder than ever before to support their patients.
“We understand people are experiencing difficulties accessing their GP surgery, and the frustrations that causes.
"We are working hard to make sure that we can continue to give the best service possible."