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Darent Valley Hospital is urging prospective patients to think before attending A&E after two weeks' of significant demand.
Despite an extensive campaign the hospital has continued to see people attending over the festive period with ailments not requiring urgent attention.
Spokesman Glyn Oakley said the period is always the busiest of the year and the past fortnight has been no different, adding the hospital is now operating at 'OPEL 4', the highest level of pressure.
Currently every hospital in Kent is at OPEL 4 level apart from East Kent which is at OPEL 3.
Mr Oakley added it was too early to say how this year compares to previous years.
A post on the hospital's Facebook page reads: "Please only come to the emergency department if you have sustained a serious injury or are in need of emergency care. We would ask you to first consider whether your condition could be dealt with more appropriately and faster at one of the alternative care centres."
It goes on to explain alternatives include a GP, the NHS 111 non-emergency phone line, pharmacists or walk-in centres, minor injuries units and urgent care centres.
Walk-in centres are staffed by health professionals who attend to patients without an appointment if there is an urgent concern.
In Gravesend a walk-in centre is available at the Whitehorse Surgery NHS, in Vale Road, Northfleet.
Trained nurses are on hand at minor injury units to assess and treat cuts, sprains, minor burns, minor dislocations of the fingers and toes, minor eye injuries and remove foreign bodies from, for example, ears and noses.
An MIU is present at Gravesham Community Hospital, in Bath Street.
Conditions such as minors cuts, bites, stings, burns, injuries, sprains, infections, minor eye injuries, fractures, minor chest, neck and back injuries and pain can be treated at urgent care centres.
Centres can be found at Queen Mary's Hospital, Frognal Avenue, Sidcup; Erith & District Hospital, Hind Crescent; and Queen Elizabeth Hospital, Stadium Road, London.