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Hospital bosses have declared a critical incident and are prioritising services to protect the most vulnerable patients.
Medway Maritime Hospital in Gillingham is currently running at "extremely high levels of occupancy" and is seeing a significant rise in demands for its services.
Patients attending A&E (accident and emergency) are rising making the department busy with staff facing challenges in discharging patients who are well enough to leave hospital, meaning there are longer waits for patients to be seen and admitted.
Medway NHS Foundation Trust says it has made the "difficult decision" to declare a critical incident which will allow hospital staff to take additional steps to maintain safe services for their patients.
This means that some non-urgent operations and outpatient appointments need to be rescheduled.
These patients are in the process of being contacted directly by trust teams and patients are advised that if they are not contacted directly to continue to turn up for your appointment.
Cancer and other urgent operations and appointments will continue to be prioritised.
The hospital said: "We appreciate that this may be disappointing for those patients whose appointments need to be moved to another date, and we would like to apologise for any inconvenience because of this.
"However, patient safety must take priority and we need to take action to make sure that those who are more clinically urgent get the help they need as quickly as possible.
"Our teams continue to work exceptionally hard; and we would like to re-assure our patients and the public that in spite of the challenges faced and some changes to non-urgent appointments, essential services remain fully open for anyone who requires urgent medical help.
"The public can help to reduce the pressures on our services by ensuring they only attend our ED for serious accidents and life-threatening emergencies.
"If you are unwell, please visit NHS 111 online, or call 111, for 24/7 advice about the most appropriate care for your needs."
You can find out the waiting times at any of the county’s minor injury units or urgent treatment centres by downloading the WaitLess app to your phone.
The app is available from the iPhone and Google play stores.