Around 5,600 patients waited beyond the targeted four-hour period to be admitted, transferred or discharged after reporting to the hospitals between Christmas Day and Hogmanay.
"That means when issues like the recent flu crisis occur, our NHS reaches breaking point".
One quarter of all patients had to wait for over four hours to get a bed in the emergency last month says the survey on performance of the A&E departments.
This compares to 92.5 per cent in the comparable week the previous year.
In addition, nearly half a million patients called the NHS 111 helpline last week, the highest number ever.
Meanwhile, nearly two-thirds of respondents (65%) said the Government was managing the current pressures on the NHS badly, 38 Degrees said.
Senior managers should consider resigning due to "their consistent failure to plan properly against a predictable winter crisis", he said.
It calls for an increase in social care funding to allow patients to be cared in the community, freeing up beds, and a review on the number of hospital beds.
"I said earlier this week and the Health Secretary said in the chamber that we apologise unreservedly to any patient who has waited longer than they should for hospital treatment or who does not get the standard of treatment that they have a right to expect, not just in winter but at any time of the year, and I do that again unequivocally today".
"And we must not simply dismiss this as the inevitable increase in pressure that winter brings".
"The situation has improved over the last week and we would like to thank our fantastic staff for their on-going efforts during this extremely challenging period and the public for their understanding and co-operation", he added.
Nationally the picture is of an ongoing crisis as the figures show waiting time targets in accident and emergency departments have hit their lowest level in 14 years, with patients "dying prematurely" in their corridors before they are seen, according to some consultants.
The letter, signed by consultants in charge of emergency departments in 68 acute hospitals across England and Wales, acknowledged the best efforts of staff, trusts and clinical commissioning groups.
They added that the NHS is "severely and chronically underfunded".
A&E workers told HuffPost UK this week that pressure on the frontline is so intense that patients are waiting 10 hours to be seen by a doctor, while doctors and nurses are suffering from anxiety and depression as a result.
"Some of our own personal experiences range from over 120 patients a day managed in corridors, some dying prematurely".
Answering questions after a speech in south London on Thursday, Mrs May said flu was putting extra pressure on services.
The higher flu rate in Scotland means the health service here is under greater pressure than the rest of the United Kingdom, she added.
Prioritisation to implement the workforce strategy that has been agreed between the Royal College and the relevant arms length bodies.
The only exceptions to this are cancer operations and what the NHS called "time-critical procedures" where the surgery has to go ahead to avoid the patient's condition deteriorating further.
The figures also showed that a further 30 patients needed intensive care.