They describe the compromise of safety at hospitals as "intolerable" and the NHS as "severely and chronically underfunding", while also publicly apologising to patients for failing to "fulfil our pledge for a safe efficient service".
"Staff up and down the country are doing a remarkable job and I am continuing to visit hospitals around the country to thank them personally for their hard work and dedication during this busy time".
The figures also showed that a further 30 patients needed intensive care.
She added: "Nevertheless, Scotland's NHS remains the best-performing NHS anywhere in the United Kingdom".
The latest figures from Public Health England (PHE) show the number of flu patients admitted to hospital were two-and-a-half times higher than at the same time past year.
There is no question that a huge amount of effort and energy has been spent both locally and nationally on drawing up plans for coping with NHS winter pressures.
Jim Crombie, deputy chief executive of NHS Lothian, said: "I would like to apologise to Mr Wilson and his family for any delays they encountered in the emergency department at the Royal Infirmary of Edinburgh".
The signatories are from hospitals including major London teaching hospitals such as the Royal Free, King's College and Guy's and St Thomas's, as well as regional trauma centres such as the University Hospitals of North Midlands NHS trust, which runs the Royal Stoke hospital, as well as several of the seven health boards in Wales. They add that this is not a report from "outliers" but most of the hospitals and trusts are facing the same problem.
As you will know a number of scientific publications have shown that crowded Emergency Departments are risky for patients. Numerous trusts we work in are in similar positions.
However analysis by the BBC showed that A&E waiting time performance in December continued to be better in Scotland than in England, where senior doctors have warned that patients are "dying in hospital corridors".
We have known for a number of years that recruitment of staff to Emergency Departments has been challenging. They have asked for infrastructure and strategies to reduce the overcrowding in the A&E departments.
NHS Providers is also calling for a full review of how well the NHS handled this winter, looking at: adequacy of bed numbers and staffing levels; efficacy of the new national planning approach; adequacy, timing and allocation of extra winter funding; system resilience; process and impact of cancelled elective operations; and the role and availability of primary care and social care, and their involvement in winter planning.
It was claimed Health Secretary Shona Robison had ignored a letter from Mr Wilson's son Michael demanding to know why his dad was left to suffer on New Year's Day.
We remain hopeful and committed to improving the care of patients in Emergency Departments throughout the UK.