Cumberland Infirmary in Carlisle and West Cumberland Hospital in Whitehaven have ranked 31st out of 138 Trusts in England for Accident and Emergency performance.
The national standard is that 95% of patients should be seen, treated, admitted or discharged in under four hours. North Cumbria University Hospitals Trust's overall performance was 92.6% in June and 93.2% in July:
Dozens of patients were left waiting more than four hours in the accident and emergency departments of hospitals in the south of Scotland last week.
The target time to admit patients is four hours, but 125 patients had to wait for longer than this.
At the Dumfries and Galloway Royal Infirmary, and Galloway Community Hospital, eight patients waited more than eight hours, while a further 94 had to wait for more than four hours.
At the Borders General Hospital, 22 patients had to wait for more than four hours, and one patient waited for more than eight hours.
Recent figures show a reported 774 attacks on staff in Accident and Emergency departments over a two year period in Scotland; The equivalent to one attack a day.
The Scottish Liberal Democrats obtained the statistics through a Freedom of Information Request.
The figures showed that in the Scottish Borders, 74 attacks took place during 2012 and 2013.
South of Scotland MSP Jim Hume says that for a small health board, that figure is "totally unacceptable".
In Dumfries and Galloway the number of attacks was much lower at 9 during one year.
Patients are being asked to 'Think twice' before visiting the accident and emergency department of their local hospital. The North Cumbria University Hospital trust are asking people to remember that A&E and 999 services are for emergency situations.
They say that A&E is the best option for life-threatening and serious emergencies, such as serious accidents and burns, breathing problems, heart attacks and strokes. For other conditions other NHS services are usually a better option.
Patients are encouraged to use services such as NHS Direct, high street pharmacies, GP practices and walk-in centres at local community hospitals for non emergency treatments.
Mike Walker, Medical Director at North Cumbria University Hospitals, said: